Suppose the continuously compounding interest rate r is constant. Given S(0), find the price of the stock after two days such that the marking to market of futures with delivery in 3 months is a dollars on day one and b dollars on day two.

6(b) Suppose that a futures price is currently £30. The risk-free interest rate is 5% per annumcontinuously compounded. A three-month American call futures option with a strike priceof £28 is worth £4. Calculate bounds for the price of a three-month American put futuresoption with a strike price of £28.

A non-dividend paying asset is current priced at $25 and the risk-free interest rate is 8% per annum. Today, you enter into a six-month futures contract to buy a unit of this asset. Three months from now the underlying price has fallen to $18 (but note that the interest rate has not moved). Which of the answers below is closest to the fall in the futures price? Use discrete discounting. Question 7Answer a. $6.50 b. $5.50 c. $7.50 d. $4.50

Suppose that a stock is currently trading at £ 38, and that the current prices for European call and put options on this stock with maturity T 10 years and identical strike price K are equal to £30 and £35, respectively. Assuming that interest is compounded annually at rate 4%, determine the strike price to the nearest pence. Do not type in the pound sign. =

D6) You use the Black Scholes model to price a Call option on a stock with discrete dividends. The dividends will be given in months 1, 5, and 9, each 3 USD. The current value of the stock is 105 USD, the strike price is 90 USD, the continuously compounded annual risk-free rate is 0.05, the volatility is 0.08, the time to maturity is 12 months. Calculate the price of the option.

Find the implied volatility (to 2 decimals, for example, �=8.23% ) of a Put option with a time to expiration of 11 months and a price of $6.13 The stock is currently trading at $47. The riskless rate is 2% per annum, and the strike/exercise price of the option is $50. Hint: compute the Put price using the same formula as in exercise 4 , as a function of the volatility �. Then use Solver to change the volatility cell in order to obtain a price of $6.13 \table[[�1=,-0.0614997,,So =,47],[�2=,,4,�=,50],[,,,�=,2%

Suppose the 6-month Mini S&P 500 futures price is 1,168.44, while the cash price is 1,150.55. What is the implied dividend yield on the S&P 500 if the risk-free interest rate is 4.3 percent? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Implied dividend yield %