Underlying asset price at current time is $100 and u(up factor in the binomial t
ID: 2782350 • Letter: U
Question
Underlying asset price at current time is $100 and u(up factor in the binomial tree) is 1.05 and d(down factor in the binomial tree) is 0.95. Exercise price is 98 and risk free rate is 0.02%. Assume one-period model. (This is questions for 21 thru 23)
21. What is the European call option price?
a) $1.51 b) $2.51 c) $3.51 d) $4.51 22.
What is the intrinsic value of the above call option?
a) $0 b) $1 c) $2 d) $3 23.
Is the call option in-the-money, at-the-money, or out-of-the money?
a) ITM b) ATM c) OTM d) None of the above
Explanation / Answer
Option C
given annual risk free rate=0.02%
So, continuous risk free=ln(1+0.02%)=0.0002=0.02%
probability of up movement, p=(e^(rt)-d)/(u-d)=(e^(0.02%*1)-0.95)/(1.05-0.95)=0.502
probability of down movement, 1-p=1-0.502=0.498
100*1.05=105..call payoff=max(105-98,0)=7
100
100*0.95=95..call payoff=max(95-98,0)=0
So, price of call=(7*p+0*(1-p))*e^(-rt)=7*0.502*e^(0.02%)=3.51
Option C
Intrinsic value=max(S-X,0)
where S is the current spot price
X is strike or exercise price
Intrinsic value=max(100-98,0)=2
Option A
As exercise price is less than current spot price, we can exercise the call option hence, it is ITM
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