Question

The current price of stock is 20TRY. The volatility is estimated by using historical data and found to be %30. Use at two step binomial tree approach to find the value of six month european put option with strike price of 21TRY. The risk free rate is %10. Would you exercise the option before expiration date if it were an american one ?

Answer 1

Risk Free Rate factor (R)=(1+10%/4)=1.025 (Since we will reach the first node after 3 month)

upward factor=(1+30%)=1.30

downward factor=(1-30%)=0.70

probability of upward movement(p)=(1.025-0.70)/(1.30-0.70)=54.16%

probability of downward movement(1-p)=(1-58.33%)=45.83%

So, after 3 month price will be either 20*1.30=26 with probability of 54.16% or 20*0.7=14 with probability 45.83%

At the end of 6 month price will go from 26 to either 26*1.3=33.8 with 54.16% probability or 26*0.70=18.2 with 45.83% probability

Or,

At the end of 6 month price will go from 14 to 14*1.3=18.2 with 54.16% probability or 14*0.7=9.8 with probability 45.83%

Expected Pay off of the put option=0+(21-18.2)*0.5416*0.4583+(21-18.2)*0.4583*.5416+(21-9.8)*0.4583*0.4583= 3.74

So, Value of European put option=3.74/1.05=3.56TRY

If the price after 3 month would have gone down to 14 after first 3 month, the I would have exercised the american put option to get a net profit of (21-14-3.56)=3.44TRY.