We model the movement of stock prices using a Binomial tree.

Each branch of the tree spans a time horizon of 5 months.

The proportional down movement on the tree (d) is 0.74.

What is the volatility of the stock implied by d? 

If your answer is (say) 40%, enter 0.40.

The volatility (sigma) of a stock is 54% per annum.

We will model stock-price movements using a Binomial tree, where each branch of the tree has a step length (delta t) of 3 months.

Calculate the proportion up movement (u) that applies to each branch of the tree.

Your answer should have at least two decimal places.

What is the upper bound of a European put option with 5 months to expiry and a strike price of $ 7.2. The underlying stock is currently trading at $ 4.5, and the risk-free rate is 5.7%.

What is the lower bound of a European put option with 1 months to expiry and a strike price of $6.9. The underlying stock is currently trading at $1.9, and the risk-free rate is 1.8%.

Do not enter the dollar sign "$".

What is the upper bound of an American put option with 6 months to expiry and a strike price of $ 7. The underlying stock is currently trading at $ 2.4, and the risk-free rate is 1.7%.

Do not enter the dollar sign "$".

What is the lower bound of an American put option with 1 months to expiry and a strike price of 14.8. The underlying stock is currently trading at 10.6, and the risk-free rate is 8.8%.

Consider a put option and a call option written on the same stock and with the same strike price. Which of the following is true?

LOL Ltd has a current share price of $60. A put option written on LOL, which has a strike price has $58 and 6 months to expiry, is trading at $3.27.

If the riskfree rate of interest is 6% pa (continuously compounded), what is the correct price for a call option on LOL with $58 strike price and 6 months to expiry?

Do not enter the dollar sign "$" in your answer. Your answer should have at least two decimal places.

LOL Ltd has a current share price of $50. A call option written on LOL, which has a strike price has $55 and 8 months to expiry, is trading at $6.29.

If the riskfree rate of interest is 7% pa (continuously compounded), what is the correct price for a put option on LOL with $55 strike price and 8 months to expiry?

Do not enter the dollar sign "$" in your answer. Your answer should have at least two decimal places.

An option has strike price of $34 and 15 months to expiry.

The current price of the underlying share is $31 and its volatility (sigma) is 42%.

The riskfree rate of interest is 6% per annum.

Calculate d1 for this option.    [your answer should have at least 2 decimal places]