Question

The risk-free rate is .10%. On 2020-04-30, TSLA traded for 524 USD. In one month, TSLA can either go up to 576.4 USD or down to 471.6 USD. Suppose that on 2020-04-30, you went short a 530.1304 USD put. What was the option premium that you paid or received?

Answer 1

Sol :

Stock current Price = 524

Expected to increase over next month to 576.40

Expected to decrease over next month to 471.60

Risk free rate = 10%

Probability of both options are

p1= {CMP(1+r)-S2} / (S1-S2)  

where,

CMP = Current CMP

S1 = High CMP as on expiry

S2 = Low CMP as on expiry

p1 = {524(1+0.10) - 471.60} / (576.40 - 471.60)

p1 = 104.8/104.8 = 1

p2 = 1-1 = 0

Option premium that is paid or received on a short 530.1304 USD put will be as follows,

Put Option premium for 576.40 = 0

Put Option premium for 530.1304 = 530.1304 - 471.60 = 58.4304

Option premium that is paid or received on a short 530.1304 USD put will be = (58.4304 x 1) / (1+0.10) = $53.12

Therefore Option premium that is received on a short 530.1304 USD put will be $53.12