What is the upper bound of an American put option with 7 months to expiry and a strike price of $ 8. The underlying stock is currently trading at $ 6.1, and the risk-free rate is 5.4%.

Do not enter the dollar sign "$".

What is the lower bound of an American put option with 10 months to expiry and a strike price of 10.3. The underlying stock is currently trading at 8.1, and the risk-free rate is 6.5%.

LOL Ltd has a current share price of $35. A put option written on LOL, which has a strike price has $38 and 3 months to expiry, is trading at $3.73.

If the riskfree rate of interest is 4% pa (continuously compounded), what is the correct price for a call option on LOL with $38 strike price and 3 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 $40. A call option written on LOL, which has a strike price has $38 and 9 months to expiry, is trading at $4.94.

If the riskfree rate of interest is 3% pa (continuously compounded), what is the correct price for a put option on LOL with $38 strike price and 9 months to expiry?

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

An option has strike price of $29 and 4 months to expiry.

The current price of the underlying share is $34 and its volatility (sigma) is 59%.

The riskfree rate of interest is 6% per annum.

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

You could answer this question using your intuition for option pricing. 

 When the stock price increases (with all else remaining the same), which of the following is true? 

The possible movement in share price over the next 12 months is depicted in the 4-step Binomial tree shown below.

Key details are:

• the proportional up and down movements on each branch of the tree are u = 1.2840 and d = 0.7788 respectively

• the riskfree interest rate is 7% pa continuously compounded

Let S_T denote the share value one year from now (far right side of the Binomial tree).

A strange derivative security is based on this share. It has a payoff = sqrt(S_T).

That is, if you buy this derivative today, one year from now you receive a payoff equal to the square root of whatever the share price is.

Required:

Using the 4-step Binomial tree, calculate the fair value of this derivative today.

Give your answer to at least 2 decimal places.

You are pricing a derivative using the risk-neutral approach on a Binomial tree.

The length of each branch in the tree (delta t) is 6 months.

The riskfree rate of interest is 5% per annum.

The proportional up movement in stock price is u = 1.6.

Calculate the risk-neutral probability (p*) that share price will move up.

Note: if the probability is (say) 51.23%, enter 0.5123

A single branch on a Binomial tree is represented by the following diagram. The riskfree rate is 4% and the branch length (delta t) = 6 months

Calculate how much money is required to invest in the bank ("B") to replicate the derivative.

Enter your answer to two decimal places.

Do not enter the dollar sign "$".

A positive (negative) number means invest (borrow).

A single branch on a Binomial tree is represented by the following diagram.

Calculate how many shares of the underlying asset (delta) are required to delta hedge.

Enter your answer to two decimal places.  If your answer is negative, then enter the negative sign.