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A bank is considering selling a European call option on a share, and wants to hedge some of its risk. The share is non-dividend paying and has the following properties: Strike price = $50 Option price = $17.91 I Underlying share price = $60 Volatility = 25% p.a. Time to expiry = 3 years The continuously compounded risk-free rate of interest is 3% p.a. and the vega for this option is $29.00. (ii) Calculate delta for this option. [1] (iii) Identify a delta-hedged replicating portfolio using the share and the risk-free asset. [2] Assume that the volatility has instantaneously increased to 27% p.a., with everything else except the option price remaining the same [2] (iv) Estimate the new option price. [Total 8]6 An experienced business person has a successful restaurant chain with five locations in two major cities. He believes that the economy is about to come out of a deep recession and has therefore decided to pursue an aggressive expansion plan with five new restaurants planned over the next 12 months. (i) List the sources of financing that the individual could use to aid the expansion. [4] The restaurant owner decides to raise a bond issue to finance the expansion. The bond issue is currently being marketed to potential investors. (11) Describe the analysis that an investor might undertake prior to investing in this bond issue. 12] [Total 16]In a computer game a player starts with three lives. Events in the game which cause the player to lose a life occur with a probability udi + o(di) in a small time interval di. However the player can also find extra lives. The probability of finding an extra life in a small time interval dr is Adr + o(di). The game ends when a player runs out of lives. (i) Outline the state space for the process which describes the number of lives a player has. [1] (ii) Draw a transition graph for the process, including the relevant transition rates. [3] (iii) Determine the generator matrix for the process. [2] (iv) Explain what is meant by a Markov jump chain. [1] (v) Determine the transition matrix for the jump chain associated with the process. [2] (vi) Determine the probability that a game ends without the player finding an extra life. [1]