TY - JOUR

T1 - Pricing options in a Markov regime-switching model with a random acceleration for the volatility

AU - Elliott, Robert J.

AU - Chan, Leunglung

AU - Siu, Tak Kuen

PY - 2016/10/1

Y1 - 2016/10/1

N2 - This article discusses option pricing in a Markov regime-switching model with a random acceleration for the volatility. A key feature of the model is that the volatility of the underlying risky security is randomly accelerated by a coefficient which is modulated by a continuous-time, finite-state Markov chain. Consequently, the degree of acceleration in volatility depends on the state of an economy represented by the state of the chain. A system of coupled partial differential equations for the prices of a standard European option over different economic states is derived. Using the homotopy analysis method originating from algebraic topology, a pricing formula for a standard European option is derived in the form of an infinite series. In addition, we give convergence conditions and compute implied volatilities using Monte-Carlo simulations. The implied volatilities can capture some important empirical features such as the implied volatility skew and smile for both VIX options and stock index options. We also provide numerical comparisons between call option prices from the first-order approximation of the proposed numerical method to those from the Monte-Carlo simulations.

AB - This article discusses option pricing in a Markov regime-switching model with a random acceleration for the volatility. A key feature of the model is that the volatility of the underlying risky security is randomly accelerated by a coefficient which is modulated by a continuous-time, finite-state Markov chain. Consequently, the degree of acceleration in volatility depends on the state of an economy represented by the state of the chain. A system of coupled partial differential equations for the prices of a standard European option over different economic states is derived. Using the homotopy analysis method originating from algebraic topology, a pricing formula for a standard European option is derived in the form of an infinite series. In addition, we give convergence conditions and compute implied volatilities using Monte-Carlo simulations. The implied volatilities can capture some important empirical features such as the implied volatility skew and smile for both VIX options and stock index options. We also provide numerical comparisons between call option prices from the first-order approximation of the proposed numerical method to those from the Monte-Carlo simulations.

UR - http://www.scopus.com/inward/record.url?scp=84991062241&partnerID=8YFLogxK

U2 - 10.1093/imamat/hxw035

DO - 10.1093/imamat/hxw035

M3 - Article

VL - 81

SP - 842

EP - 859

JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

SN - 0272-4960

IS - 5

ER -