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A portfolio of derivatives on a stock has a delta of 2400 and a gamma of –10. An option on the stock with a delta of 0.5 and a gamma of 0.04 can be traded. What position in the option is necessary to make the portfolio gamma neutral? ( )

A. Long position in 250 options
B. Short position in 250 options
C. Long position in 20 options
D. Short position in 20 options

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What is the recommended way of making interest rates a function of time in a Cox, Ross, Rubinstein tree? ( )

A. Make u a function of time
B. Make p a function of time
C. Make u and p a function of time
D. Make the lengths of the time steps unequal

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What is the recommended way of making volatility a function of time in a Cox, Ross, Rubinstein tree? ( )

A. Make u a function of time
B. Make p a function of time
C. Make u and p a function of time
D. Make the lengths of the time steps unequal

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A binomial tree prices an American option at $3.12 and the corresponding European option at $3.04. The Black-Scholes price of the European option is $2.98. What is the control variate price of the American option? ( )

A. $3.06
B. $3.18
C. $2.90
D. $3.08

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Why do traders use volatility smiles for pricing options? ( )

A. To allow for non-lognormality of the probability distribution of future asset price
Because it is consistent with recent market moves
C. As a tool to reflect their views about extreme market moves
D. Because extreme market moves are always more likely than Black-Scholes-Merton assumes

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A portfolio of derivatives on a stock has a delta of 2400 and a gamma of –10. An option on the stock with a delta of 0.5 and a gamma of 0.04 can be traded. What position in the option is necessary to make the portfolio gamma neutral? ( )

A. Long position in 250 options B. Short position in 250 options C. Long position in 20 options D. Short position in 20 options

What is the recommended way of making interest rates a function of time in a Cox, Ross, Rubinstein tree? ( )

What is the recommended way of making volatility a function of time in a Cox, Ross, Rubinstein tree? ( )

A binomial tree prices an American option at $3.12 and the corresponding European option at $3.04. The Black-Scholes price of the European option is $2.98. What is the control variate price of the American option? ( )

Why do traders use volatility smiles for pricing options? ( )

A. Long position in 250 options
B. Short position in 250 options
C. Long position in 20 options
D. Short position in 20 options