Question

Suppose you are short 50 contracts on a 2-year 50-call option on TSLA and long 10 contracts on TSLA stock. How much will your option position increase in value if TSLA stock price goes down by $1 (use negative number if value decreases).

Suppose you are short 50 contracts on a 2-year 50-call option on TSLA and long 10 contracts on TSLA stock. How much will your option position increase in value if TSLA stock price goes up by $1 (use negative number if value decreases).

TSLA stock price is currently at $800. The stock return has an annualized volatility (sigma) of 70%. The stock does not pay dividend and assume zero interest rate. Compute the Black-Merton-Scholes value on a 6-month European call option on TSLA with a strike of $1000.

TSLA stock price is currently at $800. The stock return has an annualized volatility (sigma) of 70%. The stock does not pay dividend and assume zero interest rate. Compute the Black-Merton-Scholes delta on a 6-month European call option on TSLA with a strike of $1000

Answer 1

1. A delta of 0.5 on a call option means that for a $1 decrease in price of stock the price of call decreases by $0.5. Since we are short the contract, it will increase the option position by $0.5 per contract. Hence for 50 contracts, the value will increase by 50 x 0.5 = $25.

2. A delta of 0.5 on a call option means that for a $1 increase in price of stock the price of call increases by $0.5. Since we are short the contract, it will decrease the option position by $0.5 per contract. Hence for 50 contracts, the value will decrease by 50 x 0.5 = $25 or -$25.

3. The Black- Scholes formula is given as:

Hence, putting all the values in the above formula we get the call price as = $93.06

4.

The delta of the call option is equal to N(d1). Hence, we need to calculate N(d1) as shown in the formula.

d1= [ln(0.8) + 0.49 x 0.5/2]/(0.7xsqrt(0.5)) = -0.2033

N(d1) = 1-0.591 = 0.409. This will be the delta of the call option.