Two-State Volatility Transition Pricing and Hedging of TXO Options

Abstract

The spot markets often exhibit high and low volatilities that persist for a while. We classify the spot market volatility into two states: high and low and use the Markov chain theory to construct a Two-State volatility model for pricing and hedging Taiwan stock index options (TXO). Compared to binomial option pricing model, the Two-State model is more stable in convergence and faster in early periods of convergence but is much more time-consuming as the number of periods and computations extensively increase. The growth order of total node number for quadrinomial lattice is O(n 4) while it is O(n 2) for binomial lattice. Empirically, the Taiwan stock index has high-volatility = 42.85%, low-volatility = 17.39%, and probability of being in high-volatility state = 0.3487 over the in-sample period from 1/6/1990 to 04/30/2008 according to Markov chain. Using as large as 87,160 datasets of TXO covering out-of-sample period from 05/02/2008 to 03/17/2010 and strike prices from 3600 to 8700, we demonstrated that the Two-State volatility model has the most outstanding performance in high-volatility period as applying put options for pricing and hedging. However, to avoid the cost of taxes resulting from position changes, a longer-term (e.g. 10 day) hedge is more properly than a short-term (e.g. 5 day) hedge.