Question

1)Please provide detail explanation.

i. When valuing European Vanilla Options in the Black-Scholes-Merton Model, there is one source of uncertainty. What is this uncertainty?

ii. Why does a short call position in a European vanilla option have negative delta (?)?

2. The current price of a non-dividend paying asset is $65, the riskless interest rate is 5% p.a. continuously compounded, and the option maturity is five years. What is the lower boundary for the value of a European vanilla put option with strike price of $80?

Answer 1

i. When valuing European Vanilla Options in the Black-Scholes-Merton Model, there is one source of uncertainty. What is this uncertainty?

Uncertianity is the uncertainity in the assumptions of parameters-risk free rate, volatility,

ii. Why does a short call position in a European vanilla option have negative delta (?)?

First, call price increases with increase in stock price hence short call will have negative profit if stock price increases..hence, delta of short call is negative

Second, from the formula of short call=-S*N(d1)+Ke^(-rt)N(d2)..Partially differentiaiting w.r.t. S, we get -N(d1)..As N(d1) is positive, delta will be negative

2. The current price of a non-dividend paying asset is $65, the riskless interest rate is 5% p.a. continuously compounded, and the option maturity is five years. What is the lower boundary for the value of a European vanilla put option with strike price of $80?

Lower bound=max(Xe^(-rt)-S)

=80*e^(-0.05*5)-65

=0