Double barrier options can be statically hedged by a portfolio of single barrier knockin options. The main part of the hedge automatically turns into the desired contract along the double barrier corridor extrema.

The Black Scholes Barenblatt (BSB) equation for the envelope of option prices with uncertain volatility and interest rate is derived from the Black Scholes equation with the maximum principle for diffusion equations and shown to be equivalent to a readily solvable standard Black Scholes equation...

This paper proposes a simple scheme for static hedging of defaultable contingent claims. It generalizes the techniques developed by Carr and Chou (1997), Carr and Madan (1998), and Takahashi and Yamazaki (2009a) to credit-equity models. Our scheme provides a hedging strategy across credit and...

This paper proposes an improved procedure for stochastic volatility model estimation with an application to Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) estimation. This improved procedure is composed of the following instrumental components: Fourier transform method for volatility...

We explore the class of second-order weak approximation schemes (cubature methods) for the numerical simulation of joint default probabilities in credit portfolios where the firm's asset value processes are assumed to follow the multivariate Heston stochastic volatility model. Correlation...

This paper presents a new computational scheme for an asymptotic expansion method of an arbitrary order. The asymptotic expansion method in finance initiated by Kunitomo and Takahashi (1992), Yoshida (1992b) and Takahashi (1995, 1999) is a widely applicable methodology for an analytic...

This article considers a multi-asset model based on Wishart processes that accounts for stochastic volatility and for stochastic correlations between the underlying assets, as well as between their volatilities. The model accounts for the existence of correlation term structure and correlation...

This article presents a lattice based approach for pricing contingent claims when the underlying asset evolves according to the double Heston (dH) stochastic volatility model introduced by Christoffersen et al. (2009). We discretize the continuous evolution of both squared volatilities by a...

The Hobson–Rogers model is used to price derivative securities under the no-arbitrage condition in a stochastic volatility setting, preserving the completeness of the market. Here we are studying the rate of convergence of the Euler/Monte Carlo approximations, when pricing European, Asian and...

This paper is a contribution to the pricing and hedging of options in a market where the volatility is stochastic. The new concept of relative indifference pricing is further developed. This relative price is the price at which an option trader is indifferent to trade in an additional option,...