Abstract

This paper investigates the volatility smile in the Canadian Context with the TSE-60 index and the options on this underlying asset for the period between November 5, 1999 and February 14, 2001. Evidence of the existence of a Canadian volatility smile is provided. A possible reason for the existence of the smile could be attributed to the nonconstant variance of the underlying asset, which violates one of the assumptions of the Black-Scholes model. Consequently, it would be incorrect to assume that the risk neutral probability distribution of the underlying asset is lognormal. The observation of a volatility smile justifies the use of different models to recover the risk neutral probability distribution of the underlying asset. In fact, a probability distribution different than the lognormal, should be used to calculate the expected discounted option payoffs at maturity in order to get the value of the options. In this paper, the distributions are recovered from the option prices with two models that are based on a lattice approach, namely the Jackwerth-Rubinstein (1996) and the Masson-Perrakis (2000) models. Then, the derived distributions are used to price options out-of-sample. The pricing performance of the two lattice models are compared to the Black-Sholes benchmark model. Overall, the Black-Scholes appears to outperform the Jackwerth-Rubinstein (1996) and Masson-Perrakis (2000) models. The absence of arbitrage opportunities in the sample is also verified. Only a few arbitrage opportunities, which are small in magnitude, are found in the series of options under investigation