American and European Options in Multi-Factor Jump-Diffusion Models, Near Expiry

20 Pages Posted: 26 Feb 2007

Date Written: February 24, 2007

Abstract

We derive a general formula for the time decay, theta, for out-of-the-money European options on stocks and bonds at expiry, in terms of the density of jumps and payoff. Explicit formulas are derived for the standard put and call options, exchange options in stochastic volatility and local volatility models, and options on bonds in ATSMs. Using these formulas, we show that in the presence of jumps, the limit of the no-exercise region for American options as time to expiry tends to 0 may be larger than in the pure diffusion case. In particular, for many families of non-Gaussian processes used in empirical studies of financial markets, the early exercise boundary for the American put without dividends is separated from the strike price by a non-vanishing margin.

Keywords: critical price near expiry, American puts, calls, exchange options, bond options, European options near expiry, jump-diffusions, ATSM, QTSM

JEL Classification: D81, C61

Suggested Citation

Levendorskii, Sergei Z., American and European Options in Multi-Factor Jump-Diffusion Models, Near Expiry (February 24, 2007). Available at SSRN: https://ssrn.com/abstract=965192 or http://dx.doi.org/10.2139/ssrn.965192

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
157
Abstract Views
777
rank
197,943
PlumX Metrics