Consider the following table of Put prices for an asset with S0 = 89 and no divi
ID: 2725105 • Letter: C
Question
Consider the following table of Put prices for an asset with S0 = 89 and no dividends:
Strike Premium
100 15
90 8
85 5
a) Using the above information ONLY, find the best no-arbitrage bounds on the Put premium with strike K = 95. You should specify both the lower P and upper bound P ?: P < P(95) < P ?.
b) You’re told that the premium for a Call with strike K = 90 is $10. Using this information, find the premium for a Call with strike K = 100 (hint: use put-call parity at K = 90 to find out e?rT ; then use put-call parity at K = 100).
Explanation / Answer
PART A:- (1) (2) (3) = (1) + (2)
FUTURE SPOT PRICE VALUE OF PUT (note) PREMIUM PAYOFF
100 wont be sold as it can' (15) (15)
be sold outside the market
as it is higher than strikeprice
90 5 (95 - 90) (8) (3)
85 10 (95 - 90) (5) 5
Note:- Put option is an agreement entered that the holder has right to sell the share for amount of strike price what ever the market price will be. He may sell outside i.e. not with the writer if the future spot price is more than strike price.
The no arbitrage situation arise when there is 0 payoff. hence the 0 payoff will be between 5 and -3 the Future spot price should be between 85 and 90
PART B:
PUTCALL PARITY EQUATION:
Value of call option( Vc) + present value of strike price = Value of put(Vp) + Value of spot price
by using the given information of premium $ 10 for strike price 90 we get
10 + strikeprice / ert = 8 + 89
10 + 90 / ert = 97
=>ert = 1.03
substituting ert value in below equation we get
Value of call option( Vc) + present value of strike price = Value of put(Vp) + Value of spot price
Vc + 100 / 1.03 = 15 + 89
=> value of call = 7