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Taggart Transcontinental’s stock has a volatility of 25% and a current stock price of $40 per...

Taggart Transcontinental’s stock has a volatility of 25% and a current stock price of $40 per share. Taggart pays no dividends. The risk-free interest rate is 4%.

(a). Calculate the Black-Scholes value of a one-year, at-the-money call option on Taggart stock.

The value of a one-year, at-the-money call option on Taggart stock is__________ $ (round to two decimal places)

(b). Calculate the Black-Scholes value of a one-year, at-the-money put option on Taggart stock.

The value of a one-year, at-the-money put option on Taggart stock is________ $ (round to two decimal places)

(c). Calculate the Black-Scholes value of a one-year call option on Taggart stock with a strike price of $50.

The value of a one-year call option on Taggart stock with a strike price of $50 is ____________$ (round to two decimal places)

(d). Consider a one-year, at-the-money call option on Taggart stock. Compute the effect on the price of this call option of an increase in the risk-free rate from 4% to 6%.

The effect on the price of the call option is __________$ (round to two decimal places) plug in increase or decrease__________.

(e). Consider a one-year, at-the-money call option on Taggart stock. Compute the effect on the price of this call option of an increase in the volatility from 25% to 40%.

The effect on the price of the call option is_____________ $ (round to two decimal places) plug in increase or decrease____________.

(f). Calculate the Black-Scholes Δ of a one-year, at-the-money call option on Taggart stock.

The Black-Scholes Δ of a one-year, at-the-money call option is _________ (round to four decimal places)

Solutions

Expert Solution

(a). Calculate the Black-Scholes value of a one-year, at-the-money call option on Taggart stock.

The value of a one-year, at-the-money call option on Taggart stock is $4.73

(b). Calculate the Black-Scholes value of a one-year, at-the-money put option on Taggart stock.

The value of a one-year, at-the-money put option on Taggart stock is $3.17

(c). Calculate the Black-Scholes value of a one-year call option on Taggart stock with a strike price of $50.

The value of a one-year call option on Taggart stock with a strike price of $50 is $1.47

(d). Consider a one-year, at-the-money call option on Taggart stock. Compute the effect on the price of this call option of an increase in the risk-free rate from 4% to 6%.

The effect on the price of the call option is $0.40 (5.13-4.73) Increase

(e). Consider a one-year, at-the-money call option on Taggart stock. Compute the effect on the price of this call option of an increase in the volatility from 25% to 40%.

The effect on the price of the call option is $2.30 increase

(f). Calculate the Black-Scholes Δ of a one-year, at-the-money call option on Taggart stock.

The Black-Scholes Δ of a one-year, at-the-money call option is 0.6122

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jeff jeffy answered 1 year ago

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