A barrier option is an otherwise vanilla call or put option with a strike of X but with an extra parameter B, the barrier: the option only comes into existence (is knocked in) or is terminated (is knocked out) if the spot price crosses the barrier during the life of the option. Because there is a positive probability (in either case) of worthlessness, these options are cheaper than the correspo...

This study employs the mean-variance (MV) criterion, Capital Asset Pricing Model (CAPM) statistics and stochastic dominance (SD) analysis to investigate the performance of option strategies, including writing out-of-the-money (OTM) covered call and buying in-the-money (ITM) protective put, with that of the pure-stock investment by analysing the French data in the entire 1999 year. Our results f...

Previous option pricing research typically assumes that the risk-free rate or the short rate is constant during the life of the option. In this study, we incorporate the stochastic nature of the short rate in our option valuation model and derive explicit formulas for European call and put options on a stock when the short rate follows the Merton model. Using our option model as a benchmark, ou...

This paper examines KOSPI200 index option prices in order to investigate whether index option implied volatilities foreshadowed the 1997 economic crisis in Korea. Results indicate the absence of strong fears of an impending market downturn prior to the crisis. Put option implied volatilities rose sharply as the crisis intensified, however, and the difference between put and call implied volatil...

We present new families of lower bounds for the price of the American put option on a dividend paying stock when the stock follows a log normal process and the option can be exercised continuously to a finite horizon . By put call parity, these bounds can be easily converted to bounds on the price of the Ameican call option on a dividend paying stock. By numerically optimizing these bounds, we ...

We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mell...

What is an Option? An option gives the holder the right, but not the obligation to either buy or sell some stated underlying asset at an agreed exercise price ('strike price'), either before or at some fixed date. In a legal sense an option can be categorised as a 'contingent claim' contract. The seller of an option (also known as a 'writer') grants the purchaser this right (option) in return f...