Question

Consider the binomial option pricing model. A stock is currently priced at $120 and 53 days from now the price will be either $134 or $98. The risk-free rate is 1.75%.a strike price of K = $118?

Using the Risk-Neutral Valuation model, determine the price of the Put option

Answer 1

Using the Binomial Model; Payoff table of Put option with strike price of $118:

		Price after 53 days	Value of put option [Strike price ($118) – price]
	Move up (u=134/120= 1.12)	$124	$0 (price at the strike price so option will not exercise)
Current Price of stock($120)
	Move down (d=98/120 =0.82)	$98	$20

Probability of moving up, P = e ^r*t – d / (u-d)

Where

Risk free rate, r = 1.75% per year or 0.0175

Time period, t = 53 days or 53 days/365 days = 0.145 year

Factor of moving up, u = 1.12

Factor of moving down, d = 0.82

Therefore,

P = [e^ (0.0175*0.145) – 0.82] / (1.12 -0.82)

P = 0.6027

And (1- P) = 1- 0.6027 = 0.3973 (probability of moving down)

Now the expected value of put option

= e^ - (0.0175*0.145) * (1-P) * payoff of put option

= 0.9975 *0.3973 *$20

= $ 7.9268

Therefore the price of the put option is $ 7.9268