Spread option and exchange option with stochastic interest rates

In this paper we present a simple, but new, approximation methodology for pricing a call option in a Black \& Scholes market characterized by stochastic interest rates. The method, based on a straightforward Gaussian moment matching technique applied to a conditional Black \& Scholes formula, is quite general and it applies to various models, whether affine or not. To check its accuracy and computational time, we implement it for the CIR interest rate model correlated with th...

Hamiltonian approach in quantum theory provides a new thinking for option pricing with stochastic interest rates. For barrier options, the option price changing process is similar to the infinite high barrier scattering problem in quantum mechanics; for double barrier options, the option price changing process is analogous to a particle moving in a infinite square potential well. Using Hamiltonian approach, the expressions of pricing kernels and option prices under Vasicek st...

This work studies the valuation of currency options in markets suffering from a financial crisis. We consider a European option where the underlying asset is a foreign currency. We assume that the value of the underlying asset is a stochastic process that follows a modified Black-Scholes model with an augmented stochastic volatility. Under these settings, we provide a closed form solution for the option-pricing problem on foreign currency for the European call and put options...

In the papers Carmona and Durrleman [7] and Bjerksund and Stensland [1], closed form approximations for spread call option prices were studied under the log normal models. In this paper, we give an alternative closed form formula for the price of spread call options under the log-normal models also. Our formula can be seen as a generalization of the closed-form formula presented in Bjerksund and Stensland [1] as their formula can be obtained by selecting special parameter val...

This paper presents a new model for options pricing. The Black-Scholes-Merton (BSM) model plays an important role in financial options pricing. However, the BSM model assumes that the risk-free interest rate, volatility, and equity premium are constant, which is unrealistic in the real market. To address this, our paper considers the time-varying characteristics of those parameters. Our model integrates elements of the BSM model, the Heston (1993) model for stochastic varianc...

In this paper we study the pricing of exchange options under a dynamic described by stochastic correlation with random jumps. In particular, we consider a Ornstein-Uhlenbeck covariance model with Levy Background Noise Process driven by Inverse Gaussian subordinators. We use expansion in terms of Taylor polynomials and cubic splines to approximately compute the price of the derivative contract. Our findings show that this approach provides an efficient way to compute the price...

We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed effciently through the FFT methodology thanks to the affinity of the model Our framework is also able to describe many non trivial links between FX rates and interest rates: a second calibration exercise highlights the a...

We propose a robust and stable lattice method which permits to obtain very accurate American option prices in presence of CIR stochastic interest rate without any numerical restriction on its parameters. Numerical results show the reliability and the accuracy of the proposed method.

This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented by an It\^{o}'s diffusion with time--dependent drift, and with a full matrix of correlations. It is known that prices of FX options in this model can be found by solving an associated backward partial differential equation (PDE). However, it...

We consider a method of lines (MOL) approach to determine prices of European and American exchange options when underlying asset prices are modelled with stochastic volatility and jump-diffusion dynamics. As the MOL, as with any other numerical scheme for PDEs, becomes increasingly complex when higher dimensions are involved, we first simplify the problem by transforming the exchange option into a call option written on the ratio of the yield processes of the two assets. This...