Question 42 Consider the following short put option Years to

Question 42 Consider the following short put option: Years to expiration = 4.21 Risk-free rate = 1.54% Volatility = 95.0% Underlying asset market price Strike price = $1.00 · $13.00 · What is the Vega of this position? Please answer this question to four decimal

Solution

Vega (v) can be calculated with the help of following formula

? = S *? (T/2?) *e^-(log(S/X) + (r +?^2/2) * T) ^2 / (2?^2 *T)

OR v = S *? (d1) ? (T)

Where, ? (d1) = (e^- (d1^2/2))/?2?

And d1 = (log(S/X) + (r +?^2/2) * T) / (?*?T)

Underline asset market price (S) = $13.00

Strike price (X) = $1.00

Years to expiration (T) = 4.21 years

Risk-free rate (r) = 1.54%

Volatility (?) = 95%

Value of Pi (?) = 3.14159

Therefore,

d1 = (log ($13/$1) + (0.0154 + 0.95^2/2) *4.21)/ (0.95 *?4.21)

=2.32375

And ? (d1) = (e^-(2.32375^2/2) / (?2 *3.14159)

=0.02681

Vega (v) = $13 * 0.02681 * ? (4.21)

=0.7152

Therefore Vega (v) of this position is 0.7152.