Option Pricing in Illiquid Markets with Jumps

  title={Option Pricing in Illiquid Markets with Jumps},
  author={Jos{\'e} M. T. S. Cruz and Daniel {\vS}ev{\vc}ovi{\vc}},
  journal={Applied Mathematical Finance},
  pages={395 - 415}
ABSTRACT The classical linear Black–Scholes model for pricing derivative securities is a popular model in the financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the assumption on the underlying asset price dynamics following a geometric Brownian motion. The main purpose of this paper is to generalize the classical Black–Scholes model for pricing derivative securities by taking into account feedback effects due to an… 

On solutions of a partial integro-differential equation in Bessel potential spaces with applications in option pricing models

In this paper we focus on qualitative properties of solutions to a nonlocal nonlinear partial integro-differential equation (PIDE). Using the theory of abstract semilinear parabolic equations we

Multidimensional Linear and Nonlinear Partial Integro-Differential Equation in Bessel Potential Spaces with Applications in Option Pricing

The purpose of this paper is to analyze solutions of a non-local nonlinear partial integrodifferential equation (PIDE) in multidimensional spaces. Such class of PIDE often arises in financial

Pricing vulnerable options with jump risk and liquidity risk

In this paper, we consider vulnerable options with jump risk and liquidity risk. In the proposed framework, we allow discontinuous changes in the information processes and the liquidity discount

The Optimal Rehedging Interval for the Options Portfolio within the RAPM, Taking into Account Transaction Costs and Liquidity Costs

Using the approach of L.C.G. Rogers and S. Singh, we added liquidity costs accounting to the model with risk adjusted pricing methodology (RAPM), generalized by M. Jandačka and D. Ševčovič. This



General Black-Scholes models accounting for increased market volatility from hedging strategies

Increases in market volatility of asset prices have been observed and analysed in recent years and their cause has generally been attributed to the popularity of portfolio insurance strategies for

Option pricing when underlying stock returns are discontinuous

Pricing and hedging derivative securities in markets with uncertain volatilities

We present a model for pricing and hedging derivative securities and option portfolios in an environment where the volatility is not known precisely, but is assumed instead to lie between two extreme

On the risk-adjusted pricing-methodology-based valuation of vanilla options and explanation of the volatility smile

We analyse a model for pricing derivative securities in the presence of both transaction costs as well as the risk from a volatile portfolio. The model is based on the Black-Scholes parabolic PDE

Perfect option hedging for a large trader

  • R. Frey
  • Economics
    Finance Stochastics
  • 1998
This analysis extends prior work of Jarrow to economies with continuous security trading and characterize the solution to the hedge problem in terms of a nonlinear partial differential equation and provides results on existence and uniqueness of this equation.

A Jump-Diffusion Model for Option Pricing

  • S. Kou
  • Economics
    Manag. Sci.
  • 2002
A double exponential jump-diffusion model is proposed, for the purpose of option pricing, which is simple enough to produce analytical solutions for a variety of option-pricing problems, including call and put options, interest rate derivatives, and path-dependent options.

The Feedback Effect of Hedging in Illiquid Markets

The modification of the stochastic process of the underlying asset that follows from the presence of dynamic trading strategies is derived and the nonlinear effects and the feedback from prices to trading strategy are analyzed.

Risk Management for Derivatives in Illiquid Markets: A Simulation Study

In this paper we study the hedging of derivatives in illiquid markets. More specifically we consider a model where the implementation of a hedging strategy affects the price of the underlying

The Variance Gamma Process and Option Pricing

A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. Theprocess is obtained by

Market Volatility and Feedback Effects from Dynamic Hedging

In this paper we analyze the manner in which the demand generated by dynamic hedging strategies affects the equilibrium price of the underlying asset. We derive an explicit expression for the