# A Put-Call Transformation of the Exchange Option Problem under Stochastic Volatility and Jump Diffusion Dynamics

@article{Garces2020APT, title={A Put-Call Transformation of the Exchange Option Problem under Stochastic Volatility and Jump Diffusion Dynamics}, author={Len Patrick Dominic M. Garces and G. Cheang}, journal={arXiv: Mathematical Finance}, year={2020} }

We price European and American exchange options where the underlying asset prices are modelled using a Merton (1976) jump-diffusion with a common Heston (1993) stochastic volatility process. Pricing is performed under an equivalent martingale measure obtained by setting the second asset yield process as the numeraire asset, as suggested by Bjerskund and Stensland (1993). Such a choice for the numeraire reduces the exchange option pricing problem, a two-dimensional problem, to pricing a call… Expand

#### One Citation

A numerical approach to pricing exchange options under stochastic volatility and jump-diffusion dynamics

- Economics
- 2021

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… Expand

#### References

SHOWING 1-10 OF 62 REFERENCES

Representation of exchange option prices under stochastic volatility jump-diffusion dynamics

- Economics, Mathematics
- 2020

In this article, we provide representations of European and American exchange option prices under stochastic volatility jump-diffusion (SVJD) dynamics following models by Merton [Option pricing when… Expand

The representation of American options prices under stochastic volatility and jump-diffusion dynamics

- Economics
- 2013

This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square-root process as used by Heston [Rev.… Expand

Representation of American Option Prices Under Heston Stochastic Volatility Dynamics Using Integral Transforms

- Economics
- 2010

We consider the evaluation of American options on dividend paying stocks in the case where the underlying asset price evolves according to Heston’s stochastic volatility model in (Heston, Rev.… Expand

American Call Options Under Jump‐Diffusion Processes – A Fourier Transform Approach

- Mathematics
- 2006

We consider the American option pricing problem in the case where the underlying asset follows a jump‐diffusion process. We apply the method of Jamshidian to transform the problem of solving a… Expand

The Evaluation of American Option Prices Under Stochastic Volatility and Jump-Diffusion Dynamics Using the Method of Lines

- Economics
- 2008

This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of… Expand

Pricing an American Call Under Stochastic Volatility and Interest Rates

- Business
- 2014

This chapter discusses the problem of pricing an American call option when the underlying dynamics follow the Heston’s stochastic volatility and the Cox-Ingersoll-Ross (CIR) stochastic interest rate.… Expand

Pricing exchange options with correlated jump diffusion processes

- Mathematics
- 2020

We study the applicability to energy facilities of a model for correlated Poisson processes generated by self-decomposable jumps. In this context, the implementation of our approach, both to shape… Expand

Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Thephlx Deutschemark Options

- Mathematics, Economics
- 1993

An efficient method is developed for pricing American options on combination stochastic volatility/jump-diffusion processes when jump risk and volatility risk are systematic and nondiversifiable,… Expand

Exchange Options under Jump-Diffusion Dynamics

- Economics
- 2008

This article extends the exchange option model of Margrabe, where the distributions of both stock prices are log-normal with correlated Wiener components, to allow the underlying assets to be driven… Expand

Pricing American Options Written on Two Underlying Assets

- Mathematics
- 2011

This paper extends the integral transform approach of McKean (1965) and Chiarella and Ziogas (2005) to the pricing of American options written on more than one underlying asset under the Black and… Expand