An analytical option pricing formula for mean-reverting asset with time-dependent parameter

P Nonsoong, K Mekchay, S Rujivan - The ANZIAM Journal, 2021 - cambridge.org
P Nonsoong, K Mekchay, S Rujivan
The ANZIAM Journal, 2021cambridge.org
We present an analytical option pricing formula for the European options, in which the price
dynamics of a risky asset follows a mean-reverting process with a time-dependent
parameter. The process can be adapted to describe a seasonal variation in price such as in
agricultural commodity markets. An analytical solution is derived based on the solution of a
partial differential equation, which shows that a European option price can be decomposed
into two terms: the payoff of the option at the initial time and the time-integral over the lifetime …
We present an analytical option pricing formula for the European options, in which the price dynamics of a risky asset follows a mean-reverting process with a time-dependent parameter. The process can be adapted to describe a seasonal variation in price such as in agricultural commodity markets. An analytical solution is derived based on the solution of a partial differential equation, which shows that a European option price can be decomposed into two terms: the payoff of the option at the initial time and the time-integral over the lifetime of the option driven by a time-dependent parameter. Finally, results obtained from the formula have been compared with Monte Carlo simulations and a Black–Scholes-type formula under various kinds of long-run mean functions, and some examples of option price behaviours have been provided.
Cambridge University Press
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