Question

Consider a one-step binomial tree on stock with a current price of $100 that can go either up to $115 or down to $85 in 1 year. The stock does not pay dividend and interest rates are zero. Use the tree to compute the delta of a 1-year $100-strike European put option on the stock.

Answer 1

Two Step Binomial Tree
r=	risk free rate	0%
t=	Length of time of a step=delta t	0.5
S0=	Current Stock Price	100
K=	strike price	100
Sou=	Stock price after one up step	115
Sod=	Stock price after one down step	85
fu=	Payoff from option after one step up	0
fd=	Payoff from option after one step down	15
Now delta = fu-fd/(Sou-Sod) =(0-15)/(115-85)
=-15/30=-0.5
So the delta of the put option is (-0.5)