Question

Imagine that both Microsoft stock (MSFT) and Facebook stock (FB) are currently trading at 20 USD/share. The price volatility of MSFT is significantly lower than that of FB. A call option on MSFT with a strike price of 20 USD and a time to maturity of 3 months is trading at a premium of 1.5 USD. Which of the following call options on FB could possibly be trading at the same price as the option on MSFT?

A. Call option on FB, with maturity of 3 months, and strike of 20 USD.

B. Call option on FB, with maturity of 6 months, and strike of 20 USD.

C. Call option on FB, with maturity of 2 months, and strike of 20 USD.

D. Call option on FB, with maturity of 3 months, and strike of 19 USD.

E. Call option on FB, with maturity of 3 months, and strike of 22 USD.

F. Call option on FB, with maturity of 1 month, and strike of 19 USD.

G. Call option on FB, with maturity of 4 months, and strike of 25 USD.

H. Call option on FB, with maturity of 6 months, and strike of 18 USD.

Answer 1

As call price increases with volatility, spot price, risk free rate, time to expiry and decreases with increase in strike price

We see that as spot price of both MSFT and FB is same but volatility is lower for MSFT and call with strike of 20 USD for MSFT is at 1.5 then call with strike of 20 USD for FB would trade at price higher than 1.5

So, for FB option to have the same price, either the strike would be increased or time to maturity decreased

SO we see options with expiry less than 3 months.Options satifying are Option C & F..Now we see options with strike more than 20 USD..Options satifying are Option E & G

F is ruled out because strike of 19 would give intrinsic value as 1 and 1 month time value of an in-the money call would be greater than 0.5..because from MSFT option whoseintrinsic value is zero, time value=1.5 for 3 months and hence per month time value is at least 0.5 for low volatility so F would have more than 0.5 as time value hence total value will be more than 1.5

The effect of voaltility would be predominant as vega is highest at ATM and hence the decrease in maturity from 3 to 2 wouldnt be able to lessen the premium by great extent hence, option C is also ruled out

Option E would be higher because the volatility is much higher for FB but here strike is only 10% higher..

THE answer would be OPTION G