As seen in the proof of the BSM call formula, for a call

\[N\left(d_{2}ight)=P[A(T) / F \geq K / F]=P[A(T)>K]\]

that is, \(N\left(d_{2}ight)\) is the probability that the call option finishes in the money.

(a) With \(A(0)=100, \sigma=10 \%, T=1 / 2, r=5 \%\), compute the value of the following 6-month expiry digital payoff: \(\$ 1,000,000\) if \(A(T)>\) 100 and 0 otherwise.

(b) Using same values as above, compute the value of a 6-month expiry knock-in call with payoff \(\max (0, A(T)-100)\), but only if \(A(T)>\) 110 (see last payoff in Figure 6.5).

Figure 6.5

Transcribed Image Text:

Straddle Spread Digital Strangle Ratio x2 Knock-in Collar Fly x2