assume we are in an investment universe consisting of a risk free asset with ris
ID: 2634468 • Letter: A
Question
assume we are in an investment universe consisting of a risk free asset with risk free rate of return 0; a security whose value today is $100; and a call option on that security with expiration T=1 and strike price k=150. Assume further that at T=1 the world will be in one of only three possible states, u, s, d; and that the value of the security in these three states will be $200, $100, and $50 respectively.
Use the fundamental theorem of asset pricing to find the values of c, the price of the option, for which there is no arbitrage in the system.
Explanation / Answer
Strike price =150
Value of security today =100.
Value of security at end of 1 year
payoff of call option(Strike 150)
50
0
100
0
200
50
Expected payoff((0+0+50)/3)
16.66666667
Value of call option = 16.6667*exp(-r*t)
Since risk free rate of return(r) =0
Value of call option = 16.6667*exp(0),
Now, exp(0) =1
Value of call option = 16.6667
Value of security at end of 1 year
payoff of call option(Strike 150)
50
0
100
0
200
50
Expected payoff((0+0+50)/3)
16.66666667
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.