A stock is currently trading at $S _ { 0 } = 25.85$ . It is not expected to pay dividends over the next year. You price a six-month put option on the stock with a strike of $K = 15$ using the Black-Scholes model and find the following numbers: $$\begin{array} { r l r l }
d _ { 1 } & = 2.115 & d _ { 2 } & = 1.832 \
N \left( d _ { 1 } \right) & = 0.983 & N \left( d _ { 2 } \right) & = 0.967
\end{array}$$ Given this information, the risk-neutral probability of the put finishing in the money is
A) 1.7%
B) 1.832%
C) 2.115%
D) 3.3%

Question

A stock is currently trading at $S _ { 0 } = 25.85$ . It is not expected to pay dividends over the next year. You price a six-month put option on the stock with a strike of $K = 15$ using the Black-Scholes model and find the following numbers: $$\begin{array} { r l r l } 
d _ { 1 } & = 2.115 & d _ { 2 } & = 1.832 \
N \left( d _ { 1 } \right) & = 0.983 & N \left( d _ { 2 } \right) & = 0.967
\end{array}$$ Given this information, the risk-neutral probability of the put finishing in the money is
A) 1.7%
B) 1.832%
C) 2.115%
D) 3.3%

Quizplus · Accepted Answer

The risk-neutral probability of the put option finishing in the money is given by $1 - N(d_2)$, which equals $1 - 0.967 = 0.033$ or 3.3%.

A Stock Is Currently Trading At S0=25.85S _ { 0 } = 25.85S0​=25.85

A Stock Is Currently Trading At $S _ { 0 } = 25.85$