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4,100 | Discrete Time vs Continuous Time Stock-price Dynamics and implications for Option Pricing | q-fin.PR | In the present paper we construct stock price processes with the same
marginal log-normal law as that of a geometric Brownian motion and also with
the same transition density (and returns' distributions) between any two
instants in a given discrete-time grid. We then illustrate how option prices
based on such processes... | finance |
4,101 | Constant Maturity Credit Default Swap Pricing with Market Models | q-fin.PR | In this work we derive an approximated no-arbitrage market valuation formula
for Constant Maturity Credit Default Swaps (CMCDS). We move from the CDS
options market model in Brigo (2004), and derive a formula for CMCDS that is
the analogous of the formula for constant maturity swaps in the default free
swap market unde... | finance |
4,102 | An exact formula for default swaptions' pricing in the SSRJD stochastic intensity model | q-fin.PR | We develop and test a fast and accurate semi-analytical formula for
single-name default swaptions in the context of a shifted square root jump
diffusion (SSRJD) default intensity model. The model can be calibrated to the
CDS term structure and a few default swaptions, to price and hedge other credit
derivatives consist... | finance |
4,103 | Measuring expectations in options markets: An application to the SP500 index | q-fin.PR | Extracting market expectations has always been an important issue when making
national policies and investment decisions in financial markets. In option
markets, the most popular way has been to extract implied volatilities to
assess the future variability of the underlying with the use of the Black and
Scholes formula... | finance |
4,104 | Robust pricing and hedging of double no-touch options | q-fin.PR | Double no-touch options, contracts which pay out a fixed amount provided an
underlying asset remains within a given interval, are commonly traded,
particularly in FX markets. In this work, we establish model-free bounds on the
price of these options based on the prices of more liquidly traded options
(call and digital ... | finance |
4,105 | Volatility forecasts and the at-the-money implied volatility: a multi-components ARCH approach and its relation with market models | q-fin.PR | For a given time horizon DT, this article explores the relationship between
the realized volatility (the volatility that will occur between t and t+DT),
the implied volatility (corresponding to at-the-money option with expiry at
t+DT), and several forecasts for the volatility build from multi-scales linear
ARCH process... | finance |
4,106 | BSLP: Markovian Bivariate Spread-Loss Model for Portfolio Credit Derivatives | q-fin.PR | BSLP is a two-dimensional dynamic model of interacting portfolio-level loss
and spread (more exactly, loss intensity) processes. The model is similar to
the top-down HJM-like frameworks developed by Schonbucher (2005) and
Sidenius-Peterbarg-Andersen (SPA) (2005), however is constructed as a
Markovian, short-rate intens... | finance |
4,107 | Exchangeability type properties of asset prices | q-fin.PR | In this paper we analyse financial implications of exchangeability and
similar properties of finite dimensional random vectors. We show how these
properties are reflected in prices of some basket options in view of the
well-known put-call symmetry property and the duality principle in option
pricing. A particular atten... | finance |
4,108 | Quantized Interest Rate at the Money for American Options | q-fin.PR | In this work, we expand the idea of Samuelson[3] and Shepp[2,5,6] for stock
optimization using the Bachelier model [4] as our models for the stock price at
the money (X[stock price]= K[strike price]) for the American call and put
options [1]. At the money (X= K) for American options, the expected payoff of
both the cal... | finance |
4,109 | A Simplified Approach to modeling the credit-risk of CMO | q-fin.PR | The credit crisis of 2007 and 2008 has thrown much focus on the models used
to price mortgage backed securities. Many institutions have relied heavily on
the credit ratings provided by credit agency. The relationships between
management of credit agencies and debt issuers may have resulted in conflict of
interest when ... | finance |
4,110 | Exact Pricing Asymptotics of Investment-Grade Tranches of Synthetic CDO's Part I: A Large Homogeneous Pool | q-fin.PR | We use the theory of large deviations to study the pricing of
investment-grade tranches of synthetic CDO's. In this paper, we consider a
simplified model which will allow us to introduce some of the concepts and
calculations. | finance |
4,111 | Exact Pricing Asymptotics for Investment-Grade Tranches of Synthetic CDO's. Part II: A Large Heterogeneous Pool | q-fin.PR | We use the theory of large deviations to study the pricing of
investment-grade tranches of synthetic CDO's. In this paper, we consider a
heterogeneous pool of names. Our main tool is a large-deviations analysis which
allows us to precisely study the behavior of a large amount of idiosyncratic
randomness. Our calculatio... | finance |
4,112 | Maximum Entropy Distributions Inferred from Option Portfolios on an Asset | q-fin.PR | We obtain the maximum entropy distribution for an asset from call and digital
option prices. A rigorous mathematical proof of its existence and exponential
form is given, which can also be applied to legitimise a formal derivation by
Buchen and Kelly. We give a simple and robust algorithm for our method and
compare our... | finance |
4,113 | A Review of Volatility and Option Pricing | q-fin.PR | The literature on volatility modelling and option pricing is a large and
diverse area due to its importance and applications. This paper provides a
review of the most significant volatility models and option pricing methods,
beginning with constant volatility models up to stochastic volatility. We also
survey less comm... | finance |
4,114 | Regime Switching Stochastic Volatility with Perturbation Based Option Pricing | q-fin.PR | Volatility modelling has become a significant area of research within
Financial Mathematics. Wiener process driven stochastic volatility models have
become popular due their consistency with theoretical arguments and empirical
observations. However such models lack the ability to take into account long
term and fundame... | finance |
4,115 | Credit risk modeling using time-changed Brownian motion | q-fin.PR | Motivated by the interplay between structural and reduced form credit models,
we propose to model the firm value process as a time-changed Brownian motion
that may include jumps and stochastic volatility effects, and to study the
first passage problem for such processes. We are lead to consider modifying the
standard f... | finance |
4,116 | Implied Correlation for Pricing multi-FX options | q-fin.PR | Option written on several foreign exchange rates (FXRs) depends on
correlation between the rates. To evaluate the option, historical estimates for
correlations can be used but usually they are not stable. More significantly,
pricing of the option using these estimates is usually inconsistent to the
traded vanilla contr... | finance |
4,117 | Information of Interest | q-fin.PR | A pricing formula for discount bonds, based on the consideration of the
market perception of future liquidity risk, is established. An
information-based model for liquidity is then introduced, which is used to
obtain an expression for the bond price. Analysis of the bond price dynamics
shows that the bond volatility is... | finance |
4,118 | Option pricing under Ornstein-Uhlenbeck stochastic volatility: a linear model | q-fin.PR | We consider the problem of option pricing under stochastic volatility models,
focusing on the linear approximation of the two processes known as exponential
Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit
dynamics in the regime of low fluctuations of the volatility process, under
which we ... | finance |
4,119 | Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves | q-fin.PR | We revisit the problem of pricing and hedging plain vanilla single-currency
interest rate derivatives using multiple distinct yield curves for market
coherent estimation of discount factors and forward rates with different
underlying rate tenors.
Within such double-curve-single-currency framework, adopted by the mark... | finance |
4,120 | Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes | q-fin.PR | In this paper, we obtain asymptotic formulas with error estimates for the
implied volatility associated with a European call pricing function. We show
that these formulas imply Lee's moment formulas for the implied volatility and
the tail-wing formulas due to Benaim and Friz. In addition, we analyze
Pareto-type tails o... | finance |
4,121 | Asymptotic Implied Volatility at the Second Order with Application to the SABR Model | q-fin.PR | We provide a general method to compute a Taylor expansion in time of implied
volatility for stochastic volatility models, using a heat kernel expansion.
Beyond the order 0 implied volatility which is already known, we compute the
first order correction exactly at all strikes from the scalar coefficient of
the heat kern... | finance |
4,122 | Optimal Redeeming Strategy of Stock Loans | q-fin.PR | A stock loan is a loan, secured by a stock, which gives the borrower the
right to redeem the stock at any time before or on the loan maturity. The way
of dividends distribution has a significant effect on the pricing of the stock
loan and the optimal redeeming strategy adopted by the borrower. We present the
pricing mo... | finance |
4,123 | Pricing European Options with a Log Student's t-Distribution: a Gosset Formula | q-fin.PR | The distribution of the returns for a stock are not well described by a
normal probability density function (pdf). Student's t-distributions, which
have fat tails, are known to fit the distributions of the returns. We present
pricing of European call or put options using a log Student's t-distribution,
which we call a ... | finance |
4,124 | Pricing and Hedging Asian Basket Options with Quasi-Monte Carlo Simulations | q-fin.PR | In this article we consider the problem of pricing and hedging
high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We
assume a Black-Scholes market with time-dependent volatilities and show how to
compute the deltas by the aid of the Malliavin Calculus, extending the
procedure employed by Montero and... | finance |
4,125 | Binomial Approximations for Barrier Options of Israeli Style | q-fin.PR | We show that prices and shortfall risks of game (Israeli) barrier options in
a sequence of binomial approximations of the Black--Scholes (BS) market
converge to the corresponding quantities for similar game barrier options in
the BS market with path dependent payoffs and the speed of convergence is
estimated, as well. ... | finance |
4,126 | Strict Local Martingale Deflators and Pricing American Call-Type Options | q-fin.PR | We solve the problem of pricing and optimal exercise of American call-type
options in markets which do not necessarily admit an equivalent local
martingale measure. This resolves an open question proposed by Fernholz and
Karatzas [Stochastic Portfolio Theory: A Survey, Handbook of Numerical
Analysis, 15:89-168, 2009]. | finance |
4,127 | Upper and lower bounds on dynamic risk indifference prices in incomplete markets | q-fin.PR | In the context of an incomplete market with a Brownian filtration and a fixed
finite time horizon, this paper proves that for general dynamic convex risk
measures, the buyer's and seller's risk indifference prices of a contingent
claim are bounded from below and above by the dynamic lower and upper hedging
prices, resp... | finance |
4,128 | Introduction into "Local Correlation Modelling" | q-fin.PR | In this paper we provide evidence that financial option markets for equity
indices give rise to non-trivial dependency structures between its
constituents. Thus, if the individual constituent distributions of an equity
index are inferred from the single-stock option markets and combined via a
Gaussian copula, for examp... | finance |
4,129 | A remark on Gatheral's 'most-likely path approximation' of implied volatility | q-fin.PR | We give a new proof of the representation of implied volatility as a
time-average of weighted expectations of local or stochastic volatility. With
this proof we clarify the question of existence of 'forward implied variance'
in the original derivation of Gatheral, who introduced this representation in
his book 'The Vol... | finance |
4,130 | Pricing Fixed-Income Securities in an Information-Based Framework | q-fin.PR | In this paper we introduce a class of information-based models for the
pricing of fixed-income securities. We consider a set of continuous- time
information processes that describe the flow of information about market
factors in a monetary economy. The nominal pricing kernel is at any given time
assumed to be given by ... | finance |
4,131 | A Dynamic Model for Credit Index Derivatives | q-fin.PR | We present a new model for credit index derivatives, in the top-down
approach. This model has a dynamic loss intensity process with volatility and
jumps and can include counterparty risk. It handles CDS, CDO tranches,
Nth-to-default and index swaptions. Using properties of affine models, we
derive closed formulas for t... | finance |
4,132 | Asymptotic formulae for implied volatility in the Heston model | q-fin.PR | In this paper we prove an approximate formula expressed in terms of
elementary functions for the implied volatility in the Heston model. The
formula consists of the constant and first order terms in the large maturity
expansion of the implied volatility function. The proof is based on saddlepoint
methods and classical ... | finance |
4,133 | Exotic derivatives under stochastic volatility models with jumps | q-fin.PR | In equity and foreign exchange markets the risk-neutral dynamics of the
underlying asset are commonly represented by stochastic volatility models with
jumps. In this paper we consider a dense subclass of such models and develop
analytically tractable formulae for the prices of a range of first-generation
exotic derivat... | finance |
4,134 | From the decompositions of a stopping time to risk premium decompositions | q-fin.PR | We build a general model for pricing defaultable claims. In addition to the
usual absence of arbitrage assumption, we assume that one defaultable asset (at
least) looses value when the default occurs. We prove that under this
assumption, in some standard market filtrations, default times are totally
inaccessible stoppi... | finance |
4,135 | Defining, Estimating and Using Credit Term Structures. Part 1: Consistent Valuation Measures | q-fin.PR | In this three-part series of papers, we argue that the conventional spread
measures are not well defined for credit-risky bonds and introduce a set of
credit term structures which correct for the biases associated with the
strippable cash flow valuation assumption. We demonstrate that the resulting
estimates are signif... | finance |
4,136 | Defining, Estimating and Using Credit Term Structures. Part 3: Consistent CDS-Bond Basis | q-fin.PR | In the third part of this series we introduce consistent relative value
measures for CDS-Bond basis trades using the bond-implied CDS term structure
derived from fitted survival rate curves. We explain why this measure is better
than the traditionally used Z-spread or Libor OAS and offer simplified hedging
and trading ... | finance |
4,137 | A Guide to Modeling Credit Term Structures | q-fin.PR | We give a comprehensive review of credit term structure modeling
methodologies. The conventional approach to modeling credit term structure is
summarized and shown to be equivalent to a particular type of the reduced form
credit risk model, the fractional recovery of market value approach. We argue
that the corporate p... | finance |
4,138 | Probabilities of Positive Returns and Values of Call Options | q-fin.PR | The true probability of a European call option to achieve positive return is
investigated under the Black-Scholes model. It is found that the probability is
determined by those market factors appearing in the BS formula, besides the
growth rate of stock price. Our numerical investigations indicate that the
biases of BS... | finance |
4,139 | Recovery Swaps | q-fin.PR | We derive an arbitrage free relationship between recovery swap rates, digital
default swap spreads and conventional CDS spreads, and argue that the fair
forward recovery rate used in recovery swaps must contain a convexity premium
over the expected recovery value. | finance |
4,140 | Stochastic discount factors | q-fin.PR | The valuation process that economic agents undergo for investments with
uncertain payoff typically depends on their statistical views on possible
future outcomes, their attitudes toward risk, and, of course, the payoff
structure itself. Yields vary across different investment opportunities and
their interrelations are ... | finance |
4,141 | Arbitrage Bounds for Prices of Weighted Variance Swaps | q-fin.PR | We develop robust pricing and hedging of a weighted variance swap when market
prices for a finite number of co--maturing put options are given. We assume the
given prices do not admit arbitrage and deduce no-arbitrage bounds on the
weighted variance swap along with super- and sub- replicating strategies which
enforce t... | finance |
4,142 | Option Pricing in Multivariate Stochastic Volatility Models of OU Type | q-fin.PR | We present a multivariate stochastic volatility model with leverage, which is
flexible enough to recapture the individual dynamics as well as the
interdependencies between several assets while still being highly analytically
tractable.
First we derive the characteristic function and give conditions that ensure
its an... | finance |
4,143 | A comprehensive method for exotic option pricing | q-fin.PR | This work illustrates how several new pricing formulas for exotic options can
be derived within a Levy framework by employing a unique pricing expression.
Many existing pricing formulas of the traditional Gaussian model are obtained
as a by-product. | finance |
4,144 | Security Pricing with Information-Sensitive Discounting | q-fin.PR | In this paper incomplete-information models are developed for the pricing of
securities in a stochastic interest rate setting. In particular we consider
credit-risky assets that may include random recovery upon default. The market
filtration is generated by a collection of information processes associated
with economic... | finance |
4,145 | The impact of uncertainties on the pricing of contingent claims | q-fin.PR | We study the effect of parameters uncertainties on a stochastic diffusion
model, in particular the impact on the pricing of contingent claims, thanks to
Dirichlet Forms methods. We apply recent techniques, developed by Bouleau, to
hedging procedures in order to compute the sensitivities of SDE trajectories
with respect... | finance |
4,146 | Pricing options in illiquid markets: optimal systems, symmetry reductions and exact solutions | q-fin.PR | We study a class of nonlinear pricing models which involves the feedback
effect from the dynamic hedging strategies on the price of asset introduced by
Sircar and Papanicolaou. We are first to study the case of a nonlinear demand
function involved in the model. Using a Lie group analysis we investigate the
symmetry pro... | finance |
4,147 | A model-insensitive determination of First-hitting-time densities with Application to Equity default-swaps | q-fin.PR | Equity default-swaps pay the holder a fixed amount of money when the
underlying spot level touches a (far-down) barrier during the life of the
instrument. While most pricing models give reasonable results when the barrier
lies within the range of liquidly traded strikes of plain-vanilla option
prices, the situation is ... | finance |
4,148 | Student's t-Distribution Based Option Sensitivities: Greeks for the Gosset Formulae | q-fin.PR | European options can be priced when returns follow a Student's
t-distribution, provided that the asset is capped in value or the distribution
is truncated. We call pricing of options using a log Student's t-distribution a
Gosset approach, in honour of W.S. Gosset. In this paper, we compare the greeks
for Gosset and Bla... | finance |
4,149 | Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model | q-fin.PR | Our derivation of the distribution function for future returns is based on
the risk neutral approach which gives a functional dependence for the European
call (put) option price, C(K), given the strike price, K, and the distribution
function of the returns. We derive this distribution function using for C(K) a
Black-Sc... | finance |
4,150 | Variance dispersion and correlation swaps | q-fin.PR | In the recent years, banks have sold structured products such as worst-of
options, Everest and Himalayas, resulting in a short correlation exposure. They
have hence become interested in offsetting part of this exposure, namely buying
back correlation. Two ways have been proposed for such a strategy : either pure
correl... | finance |
4,151 | Consistent Valuation of Bespoke CDO Tranches | q-fin.PR | This paper describes a consistent and arbitrage-free pricing methodology for
bespoke CDO tranches. The proposed method is a multi-factor extension to the
(Li 2009) model, and it is free of the known flaws in the current standard
pricing method of base correlation mapping. This method assigns a distinct
market factor to... | finance |
4,152 | Valuation Bound of Tranche Options | q-fin.PR | We performed a comprehensive analysis on the price bounds of CDO tranche
options, and illustrated that the CDO tranche option prices can be effectively
bounded by the joint distribution of default time (JDDT) from a default time
copula. Systemic and idiosyncratic factors beyond the JDDT only contribute a
limited amount... | finance |
4,153 | A Dynamic Correlation Modelling Framework with Consistent Stochastic Recovery | q-fin.PR | This paper describes a flexible and tractable bottom-up dynamic correlation
modelling framework with a consistent stochastic recovery specification. The
stochastic recovery specification only models the first two moments of the spot
recovery rate as its higher moments have almost no contribution to the loss
distributio... | finance |
4,154 | Discrete tenor models for credit risky portfolios driven by time-inhomogeneous Lévy processes | q-fin.PR | The goal of this paper is to specify dynamic term structure models with
discrete tenor structure for credit portfolios in a top-down setting driven by
time-inhomogeneous L\'evy processes. We provide a new framework, conditions for
absence of arbitrage, explicit examples, an affine setup which includes
contagion and pri... | finance |
4,155 | Good-deal bounds in a regime-switching diffusion market | q-fin.PR | We consider option pricing in a regime-switching diffusion market. As the
market is incomplete, there is no unique price for a derivative. We apply the
good-deal pricing bounds idea to obtain ranges for the price of a derivative.
As an illustration, we calculate the good-deal pricing bounds for a European
call option a... | finance |
4,156 | Credit Risk, Market Sentiment and Randomly-Timed Default | q-fin.PR | We propose a model for the credit markets in which the random default times
of bonds are assumed to be given as functions of one or more independent
"market factors". Market participants are assumed to have partial information
about each of the market factors, represented by the values of a set of market
factor informa... | finance |
4,157 | Interest-Rate Modeling with Multiple Yield Curves | q-fin.PR | The crisis that affected financial markets in the last years leaded market
practitioners to revise well known basic concepts like the ones of discount
factors and forward rates. A single yield curve is not sufficient any longer to
describe the market of interest rate products. On the other hand, using
different yield c... | finance |
4,158 | Exact Pricing and Hedging Formulas of Long Dated Variance Swaps under a $3/2$ Volatility Model | q-fin.PR | This paper investigates the pricing and hedging of variance swaps under a
$3/2$ volatility model. Explicit pricing and hedging formulas of variance swaps
are obtained under the benchmark approach, which only requires the existence of
the num\'{e}raire portfolio. The growth optimal portfolio is the num\'{e}raire
portfol... | finance |
4,159 | Pricing in an equilibrium based model for a large investor | q-fin.PR | We study a financial model with a non-trivial price impact effect. In this
model we consider the interaction of a large investor trading in an illiquid
security, and a market maker who is quoting prices for this security. We assume
that the market maker quotes the prices such that by taking the other side of
the invest... | finance |
4,160 | Asymptotic equivalence in Lee's moment formulas for the implied volatility and Piterbarg's conjecture | q-fin.PR | The asymptotic behavior of the implied volatility associated with a general
call pricing function has been extensively studied in the last decade. The main
topics discussed in this paper are Lee's moment formulas for the implied
volatility, and Piterbarg's conjecture, describing how the implied volatility
behaves in th... | finance |
4,161 | Models of self-financing hedging strategies in illiquid markets: symmetry reductions and exact solutions | q-fin.PR | We study the general model of self-financing trading strategies in illiquid
markets introduced by Schoenbucher and Wilmott, 2000. A hedging strategy in the
framework of this model satisfies a nonlinear partial differential equation
(PDE) which contains some function g(alpha). This function is deep connected to
an utili... | finance |
4,162 | BSDEs with time-delayed generators of a moving average type with applications to non-monotone preferences | q-fin.PR | In this paper we consider backward stochastic differential equations with
time-delayed generators of a moving average type. The classical framework with
linear generators depending on $(Y(t),Z(t))$ is extended and we investigate
linear generators depending on $(\frac{1}{t}\int_0^tY(s)ds,
\frac{1}{t}\int_0^tZ(s)ds)$. We... | finance |
4,163 | Perpetual Cancellable American Call Option | q-fin.PR | This paper examines the valuation of a generalized American-style option
known as a Game-style call option in an infinite time horizon setting. The
specifications of this contract allow the writer to terminate the call option
at any point in time for a fixed penalty amount paid directly to the holder.
Valuation of a pe... | finance |
4,164 | Asset pricing with random information flow | q-fin.PR | In the information-based approach to asset pricing the market filtration is
modelled explicitly as a superposition of signals concerning relevant market
factors and independent noise. The rate at which the signal is revealed to the
market then determines the overall magnitude of asset volatility. By letting
this inform... | finance |
4,165 | Analytical and Numerical Approaches to Pricing the Path-Dependent Options with Stochastic Volatility | q-fin.PR | In this paper new analytical and numerical approaches to valuating
path-dependent options of European type have been developed. The model of
stochastic volatility as a basic model has been chosen. For European options we
could improve the path integral method, proposed B. Baaquie, and generalized it
to the case of path... | finance |
4,166 | American Options Pricing under Stochastic Volatility: Approximation of the Early Exercise Surface and Monte Carlo Simulations | q-fin.PR | The aim of this study was to develop methods for evaluating the
American-style option prices when the volatility of the underlying asset is
described by a stochastic process. As part of this problem were developed
techniques for modeling the early exercise surface of the American option.
These methods of present work a... | finance |
4,167 | Information-based models for finance and insurance | q-fin.PR | In financial markets, the information that traders have about an asset is
reflected in its price. The arrival of new information then leads to price
changes. The `information-based framework' of Brody, Hughston and Macrina (BHM)
isolates the emergence of information, and examines its role as a driver of
price dynamics.... | finance |
4,168 | On Calibrating Stochastic Volatility Models with time-dependent Parameters | q-fin.PR | We consider stochastic volatility models using piecewise constant parameters.
We suggest a hybrid optimization algorithm for fitting the models to a
volatility surface and provide some numerical results. Finally, we provide an
outlook on how to further improve the calibration procedure. | finance |
4,169 | Do your volatility smiles take care of extreme events? | q-fin.PR | In the Black-Scholes context we consider the probability distribution
function (PDF) of financial returns implied by volatility smile and we study
the relation between the decay of its tails and the fitting parameters of the
smile. We show that, considering a scaling law derived from data, it is
possible to get a new f... | finance |
4,170 | A la Carte of Correlation Models: Which One to Choose? | q-fin.PR | In this paper we propose a copula contagion mixture model for correlated
default times. The model includes the well known factor, copula, and contagion
models as its special cases. The key advantage of such a model is that we can
study the interaction of different models and their pricing impact.
Specifically, we model... | finance |
4,171 | Parsimonious HJM Modelling for Multiple Yield-Curve Dynamics | q-fin.PR | For a long time interest-rate models were built on a single yield curve used
both for discounting and forwarding. However, the crisis that has affected
financial markets in the last years led market players to revise this
assumption and accommodate basis-swap spreads, whose remarkable widening can no
longer be neglecte... | finance |
4,172 | Dangers of Bilateral Counterparty Risk: the fundamental impact of closeout conventions | q-fin.PR | We analyze the practical consequences of the bilateral counterparty risk
adjustment. We point out that past literature assumes that, at the moment of
the first default, a risk-free closeout amount will be used. We argue that the
legal (ISDA) documentation suggests in many points that a substitution closeout
should be u... | finance |
4,173 | A finite dimensional approximation for pricing moving average options | q-fin.PR | We propose a method for pricing American options whose pay-off depends on the
moving average of the underlying asset price. The method uses a finite
dimensional approximation of the infinite-dimensional dynamics of the moving
average process based on a truncated Laguerre series expansion. The resulting
problem is a fin... | finance |
4,174 | Risk-Neutral Pricing of Financial Instruments in Emission Markets: A Structural Approach | q-fin.PR | We present a novel approach to the pricing of financial instruments in
emission markets, for example, the EU ETS. The proposed structural model is
positioned between existing complex full equilibrium models and pure reduced
form models. Using an exogenously specified demand for a polluting good it
gives a causal explan... | finance |
4,175 | A unified approach to determining the early exercise boundary position at expiry for American style of general class of derivatives | q-fin.PR | In this paper, we present a new method for calculating the limit of early
exercise boundary at expiry. We price American style of general derivative
using a formula expressed as a sum of the value of European style of derivative
and so called American premium. We use the latter expression to calculate an
analytic formu... | finance |
4,176 | The Impossible Trio in CDO Modeling | q-fin.PR | We show that stochastic recovery always leads to counter-intuitive behaviors
in the risk measures of a CDO tranche - namely, continuity on default and
positive credit spread risk cannot be ensured simultaneously. We then propose a
simple recovery variance regularization method to control the magnitude of
negative credi... | finance |
4,177 | Pricing and Hedging in Affine Models with Possibility of Default | q-fin.PR | We propose a general framework for the simultaneous modeling of equity,
government bonds, corporate bonds and derivatives. Uncertainty is generated by
a general affine Markov process. The setting allows for stochastic volatility,
jumps, the possibility of default and correlation between different assets. We
show how to... | finance |
4,178 | Financial markets with volatility uncertainty | q-fin.PR | We investigate financial markets under model risk caused by uncertain
volatilities. For this purpose we consider a financial market that features
volatility uncertainty. To have a mathematical consistent framework we use the
notion of G-expectation and its corresponding G-Brownian motion recently
introduced by Peng (20... | finance |
4,179 | Path integral approach to the pricing of timer options with the Duru-Kleinert time transformation | q-fin.PR | In this paper, a time substitution as used by Duru and Kleinert in their
treatment of the hydrogen atom with path integrals is performed to price timer
options under stochastic volatility models. We present general pricing formulas
for both the perpetual timer call options and the finite time-horizon timer
call options... | finance |
4,180 | A Family of Maximum Entropy Densities Matching Call Option Prices | q-fin.PR | We investigate the position of the Buchen-Kelly density in a family of
entropy maximising densities which all match European call option prices for a
given maturity observed in the market. Using the Legendre transform which links
the entropy function and the cumulant generating function, we show that it is
both the uni... | finance |
4,181 | Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR | q-fin.PR | We present a quantitative study of the markets and models evolution across
the credit crunch crisis. In particular, we focus on the fixed income market
and we analyze the most relevant empirical evidences regarding the divergences
between Libor and OIS rates, the explosion of Basis Swaps spreads, and the
diffusion of c... | finance |
4,182 | Model independent hedging strategies for variance swaps | q-fin.PR | A variance swap is a derivative with a path-dependent payoff which allows
investors to take positions on the future variability of an asset. In the
idealised setting of a continuously monitored variance swap written on an asset
with continuous paths it is well known that the variance swap payoff can be
replicated exact... | finance |
4,183 | Power Series Representations for European Option Prices under Stochastic Volatility Models | q-fin.PR | In the context of stochastic volatility models, we study representation
formulas in terms of expectations for the power series' coefficients associated
to the call price-function. As in a recent paper by Antonelli and Scarlatti the
expansion is done w.r.t. the correlation between the noises driving the
underlying asset... | finance |
4,184 | Exercise Boundary of the American Put Near Maturity in an Exponential Lévy Model | q-fin.PR | We study the behavior of the critical price of an American put option near
maturity in the exponential L\'evy model when the underlying stock pays
dividends at a continuous rate. In particular, we prove that, in situations
where the limit of the critical price is equal to the stock price, the rate of
convergence to the... | finance |
4,185 | Erratum for: Smile dynamics -- a theory of the implied leverage effect | q-fin.PR | We correct a mistake in the published version of our paper. Our new
conclusion is that the "implied leverage effect" for single stocks is
underestimated by option markets for short maturities and overestimated for
long maturities, while it is always overestimated for OEX options, except for
the shortest maturities wher... | finance |
4,186 | Calibration of Chaotic Models for Interest Rates | q-fin.PR | In this paper we calibrate chaotic models for interest rates to market data
using a polynomial-exponential parametrization for the chaos coefficients. We
identify a subclass of one-variable models that allow us to introduce
complexity from higher order chaos in a controlled way while retaining
considerable analytic tra... | finance |
4,187 | Theory of Information Pricing | q-fin.PR | In financial markets valuable information is rarely circulated homogeneously,
because of time required for information to spread. However, advances in
communication technology means that the 'lifetime' of important information is
typically short. Hence, viewed as a tradable asset, information shares the
characteristics... | finance |
4,188 | Default and Systemic Risk in Equilibrium | q-fin.PR | We develop a finite horizon continuous time market model, where risk averse
investors maximize utility from terminal wealth by dynamically investing in a
risk-free money market account, a stock written on a default-free dividend
process, and a defaultable bond, whose prices are determined via equilibrium.
We analyze fi... | finance |
4,189 | Probability-free pricing of adjusted American lookbacks | q-fin.PR | Consider an American option that pays G(X^*_t) when exercised at time t,
where G is a positive increasing function, X^*_t := \sup_{s\le t}X_s, and X_s
is the price of the underlying security at time s. Assuming zero interest
rates, we show that the seller of this option can hedge his position by trading
in the underlyi... | finance |
4,190 | Pricing Variable Annuity Contracts with High-Water Mark Feature | q-fin.PR | Variable annuities (VA) are popular insurance products. VAs provides the
insured with a guaranteed accumulation rate on their premium at maturity. In
addition, the insured may receive extra benefit if returns of underlying funds
are high enough. Here we consider a special case of VA with high-water mark
feature and Gua... | finance |
4,191 | Time-Consistent and Market-Consistent Evaluations | q-fin.PR | We consider evaluation methods for payoffs with an inherent financial risk as
encountered for instance for portfolios held by pension funds and insurance
companies. Pricing such payoffs in a way consistent to market prices typically
involves combining actuarial techniques with methods from mathematical finance.
We prop... | finance |
4,192 | Time-Consistent Actuarial Valuations | q-fin.PR | Recent theoretical results establish that time-consistent valuations (i.e.
pricing operators) can be created by backward iteration of one-period
valuations. In this paper we investigate the continuous-time limits of
well-known actuarial premium principles when such backward iteration procedures
are applied. We show tha... | finance |
4,193 | The Small and Large Time Implied Volatilities in the Minimal Market Model | q-fin.PR | This paper derives explicit formulas for both the small and large time limits
of the implied volatility in the minimal market model. It is shown that
interest rates do impact on the implied volatility in the long run even though
they are negligible in the short time limit. | finance |
4,194 | Two-factor capital structure models for equity and credit | q-fin.PR | We extend the now classic structural credit modeling approach of Black and
Cox to a class of "two-factor" models that unify equity securities such as
options written on the stock price, and credit products like bonds and credit
default swaps. In our approach, the two sides of the stylized balance sheet of
a firm, namel... | finance |
4,195 | Critical Analysis of the Binomial-Tree approach to Convertible Bonds in the framework of Tsiveriotis-Fernandes model | q-fin.PR | In the present paper we show that the Binomial-tree approach for pricing,
hedging, and risk assessment of Convertible bonds in the framework of the
Tsiveriotis-Fernandes model has serious drawbacks. Key words: Convertible
bonds, Binomial tree, Tsiveriotis-Fernandes model, Convertible bond pricing,
Convertible bond Gree... | finance |
4,196 | Time Consistent Bid-Ask Dynamic Pricing Mechanisms for Contingent Claims and Its Numerical Simulations Under Uncertainty | q-fin.PR | We study time consistent dynamic pricing mechanisms of European contingent
claims under uncertainty by using G framework introduced by Peng ([24]). We
consider a financial market consisting of a riskless asset and a risky stock
with price process modelled by a geometric generalized G-Brownian motion, which
features the... | finance |
4,197 | Asymptotic Expansions of the Lognormal Implied Volatility : A Model Free Approach | q-fin.PR | We invert the Black-Scholes formula. We consider the cases low strike, large
strike, short maturity and large maturity. We give explicitly the first 5 terms
of the expansions. A method to compute all the terms by induction is also
given. At the money, we have a closed form formula for implied lognormal
volatility in te... | finance |
4,198 | A Note on the Equivalence between the Normal and the Lognormal Implied Volatility : A Model Free Approach | q-fin.PR | First, we show that implied normal volatility is intimately linked with the
incomplete Gamma function. Then, we deduce an expansion on implied normal
volatility in terms of the time-value of a European call option. Then, we
formulate an equivalence between the implied normal volatility and the
lognormal implied volatil... | finance |
4,199 | Credit derivatives pricing with default density term structure modelled by Lévy random fields | q-fin.PR | We model the term structure of the forward default intensity and the default
density by using L\'evy random fields, which allow us to consider the credit
derivatives with an after-default recovery payment. As applications, we study
the pricing of a defaultable bond and represent the pricing kernel as the
unique solutio... | finance |
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