Question

14. The current price of a non-dividend paying stock is 40 and the continuously compounded risk-free interest rate is 8%. You are given that the price of a 35-strike call option is 3.35 higher than the price of a 40-strike call option, where both options expire in 3 months. Calculate the amount by which the price of an otherwise equivalent 40-strike put option exceeds the price of an otherwise equivalent 35-strike put option. (A) B) 1.55 1.65 1.75 3.25 3.35

Answer 1

The answer is option - A) 1.55

the calculation below contains the value "e" which is the factor used for the calculation of present value while continuous compounding situation. the value of e is 2.7183.

and refer in below answer e^(8%)(3/12) means the discounting factor which is CONTINUOUS COMPOUNDING at 8% per annum INTEREST RATE for a period of 3 MONTHS.

from the given data, two equations for two situations were derived by using put - call parity theorem and those two equations were subtracted to get the required answer.

Assume the values : spot price. - $ Present value of x x = Strike Prices = Present Value of stoike Price call option price at Put option price at 35 strike c, 35 strike & Pi call option price at 40 strike - C₂ put option price at 40 strike - P. Put - Call Parity Theorem: ct Pv(x) = Pts, where c= call option price PV(x) = Present Value of strike Price P= Put option price S = spot price (current Price Now, substituting our data in the put - call Pasity A at strike - 35 . i.e. x= 35 G+ PV(x) = Pits » C,+ PV of 35 = P + 40 - Ct = P + 40

35 G-P 40 - 20.08)(0,25) 35 = 40 - 6.02) 35 - 40 - (2.71833-03 35 - 40 -110202 40-34.31 C-P 5.69 - Equation & ® at strike Price - 40 -, i.e. x = 40 G+ PV(x) = P₂ + S + Prof 40 P₂ + 40 + 20%CEM P+40 (+ 40 = P2 +40 ₂ - P = 40 - 190002 (₂ - P2 = 40 - 39.21 C₂-P2 a 0.79 - Equation ② Given values in in question c - C₂ = 3.35 Now, Equation ④ (-) Equation 6 (6,- P.) - (C₂-P2) = 5.69 -0.79 7 1.0202

- C-P,- (+ P2 = 4.9 (C,-(₂) + (P2 - P.) = 4.9 - 3.35 + (P2 - P.) = 4.9 - P2-P, è 4.9-3.35 - P.₂ -P, = 1.55 (Put option price I put option I at 40-strike) - (price at = 1.55 = 1.55 35-strike 1.e. the price of 40-strike put option exceeds the price of on 35-strike put option by 1.55