Question

1. A stock price is currently $50. It is known that at the end of one year it will be either $40 and $60. The exercise price of a one-year European call option is $55. The risk-free interest rate is 5% per annum.

1. Construct a binomial tree to show the payoff of the call option at the expiration date. (5%)
2. Based on the binomial tree model, what is the value of the call option? (15%)
3. Address the relation between the binomial tree model and the Black-Scholes model. (5%)

Answer 1

c) Relationship between binomial model and black scholars model is these both models are mostly adopted valuation model for options. The model will calculate option premium or value of option whether call or put. These methods consider probability of prices when compared to other models. The models consider risk free rate, volatility of prices.the binomial considers separate time approximation to continuos process of blackscholes. In some times binomial considers the lognormal distribution as used in blackscholes model. When the period increases in binomial for simplification uses blackscholes Formula in the absence of dividend in European option