Critically discuss how the binomial model can be linked to the Black-Scholes-Merton option pricing formula.

QUESTION 1a.Using the following information, calculate the price of a 12-month long putoption using a two-step binomial tree procedure. S0= £20, K = £21, r = 5% (annual), σ = 40% (annual).You have the following equations:𝑝=𝑎−𝑑𝑢−𝑑(1)𝑎=𝑒𝑟∆𝑡(2)𝑢=𝑒𝜎√∆𝑡(3)𝑑=1𝑢(4)𝑓=[𝑝𝑓𝑢+(1−𝑝)𝑓𝑑]𝑒−𝑟∆𝑡(5)(40% question weight)b.Critically discuss how the binomial model can be linked to the Black-Scholes-Merton option pricing formula.(30% question weight)c.Critically discuss the concept of Option Delta.(30%question weight)
Trowch drosodd / Turn over

QUESTION 3a.Provide a detailed proof and explanation of Put-Call Parity, using the synthetic forward contract as the basis for your answer. (50%question weight)b.A speculator has approached you because of your expertise in option trading. They want to speculate on the stock price of Breeze PLCover the next 2 months. They are notsure which way the price is going to move, i.e.,either up or down, but they are quite certain the price will deviate substantially from the current price, S0= £100. Specifically, the speculator thinks the price will be either above £110or below £90at maturity. The speculator is interested in a strategy thatis either:i) a short butterfly position that pays fixed amount of £5,000 if ST> £110, or ST< £90; or ii) astrangle position that paysanincreasing amount the smaller (larger) STisbelow (above) £90 (£110). For the strangle position the speculator is willing to spend £5,000. Using the following options, design a short butterfly strategy and a strangle position that can be offered to the speculator. You should clearly explain the risk that the speculator is taking should they decide to entereither position. Your answers should include a detailed payoff diagram and/or payoff table for both strategies. Option typeStrikeOption Price2-month Call£90£0.52-month Call£100£0.32-month Call£110£0.22-month Put£90£0.3(50%question weight)
Diwedd Papur Arholiad / End of Exam Script

QUESTION 4a.Kermit PLCand Cintron PLChave been offered the following rates per annum on a £10 million 5-year loan:Fixed rateFloating rateKermit PLC5%LIBOR +0.1%Cintron PLC6.4%LIBOR +0.6%Kermit PLCrequires a floating-rate loan, andCintron PLCrequires a fixed-rate loan. Design a swap that will net a bank, acting as an intermediary, 0.1% per annum and that will appear equally attractive to both companies. (30%question weight)b.Construct a table displaying the cashflows ofKermit PLC, CintronPLC, and the bank.Assume payments are made semi-annually, and that LIBOR isfixed at4.2% throughout the life of the swap. (30%question weight)c.Critically discuss why the 10-year LIBOR rates are higher than the 10-year swap rate