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...

In this paper we study the pricing and hedging of options on realized variance in the 3/2 non-affine stochastic volatility model, by developing efficient transform based pricing methods. This non-affine model gives prices of options on realized variance which allow upward sloping implied...

A bank's stock price is modeled as a call option on the spread of random assets over random liabilities. The logarithm of assets and liabilities are jointly modeled as driven by four variance gamma processes and this model is estimated by calibrating to quoted equity options seen as compound...

We present a new approach to the pricing of catastrophe event derivatives that does not assume a fully diversifiable event risk. Instead, we assume that the event occurrence and intensity affect the return of the market portfolio of an agent that trades in the event derivatives. Based on this...

In this paper, we consider the numerical approximation of the prices of vanilla options in a displaced-lognormal Heston model. First of all, we derive an alternative representation of option prices which facilitates robust numerical approximation including the case where the local volatility is...

This paper conducts a thorough and detailed investigation on the implications of stochastic volatility and random jump on option prices. Both stochastic volatility and jump-diffusion processes admit asymmetric and fat-tailed distribution of asset returns and thus have similar impact on option...

In this paper, we solve the problem of solution of stochastic volatility models in which the volatility diffusion can be solved by a one dimensional Fokker-planck equation. We use one dimensional transition probabilities for the evolution of PDE of variance. We also find dynamics of evolution of...

This paper considers the problem of European option pricing in the presence of proportional transaction costs when the price of the underlying follows a jump diffusion process. Using an approach that is based on maximization of the expected utility of terminal wealth, we transform the option...

In this paper we derive an easily computed approximation of Rogers and Shi's lower bound for a local volatility jump-diffusion model and then use it to approximate European basket option values. If the local volatility function is time independent then there is a closed-form expression for the...

Exponential Lévy processes can be used to model the evolution of various financial variables such as FX rates, stock prices, etc. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes, and the corresponding implied volatility surfaces...