Because Country A has no domestic sources of wood, it imports all its wood from
wood-producing countries. If the price of wood in wood-producing countries rises
substantially, which of the following is most likely to occur?
A Country A will import more wood to meet rising demand.
B Country A will impose a tariff on wood imports.
Housing prices in Country A will increase as wood imports become more expensive.
D Profits in other wood-producing countries will increase because of increased exports
to Country A.
Consider an option on a dividend paying stock whose price S follows a continuous random walk. A traded asset X, whose value depends only on S, is being valued by the binomial tree method with n discrete time steps and a risk- neutral probability p. (@) (a) Explain how, for sufficiently large n, the binomial tree method evaluation achieves a good estimate of the true value of X. (b) Draw a simple diagram to illustrate how the binomial tree would be adjusted to allow for the payment of a known dividend amount D at time interval t = 2. [5] "Finite difference" (FD) methods can be used to obtain an approximate numerical solution to the stochastic partial differential equation for X. (ii) (a) Describe and briefly compare two distinct FD methods. (b) Give the initial and boundary conditions for the FD valuation in the case where X is a two-year American call option on the stock.A trader is considering pricing options on a total [earn equity index whose value at time r is 3(3). The continuously compounded riskfree rate is r. She has suggested an alternative approach to estimating an implied volatility matrix as an input in the BlackScholes pricing formula. She proposes to derive the riskneutral probability distribution for rture values of 3 directly and use this as an input in an adapted version of the formula. Denote by S, it} the risk-neutral probability distribution of S at time t, and by PX, t) the price ofa European put option on the index with expiry time I and strike X. (i) {a} State (in integral fmm) a formula for Pg: 2') in terms ems, r)- 2 {11) Hence demonstrate that f {X ,1) = a\" 2X}: [3] {ii} {a} Discuss how in practice the expression in part (i)(b} couid be used to derive the riskneutral probability distribution S, if). (b) Assess the suitability of this approach for the daily pricing of the trader's options. [3"] A life insurance company has written policies linked to the equity index. These policies have investment guarantees with a wide range of terms and strikes. {iii} Discuss whether the riskneutral probability distribution might be suitable for use in the insurance companyls year end nancial reporting. [2] A "chooser" option is an option where, after a specified period of time, the holder can choose whether the option is a call or a put. Consider a chooser option on a non-income bearing security of price S with a choice at time 7 between two European options both with maturity 7, and strike K. (1) Show how this chooser option can be considered as being the sum of two components: a call with strike K and maturity 72, and a put with strike Ke "(271) and maturity T1- [2] (11) Sketch six graphs of the chooser option and its two components, showing the movement of option value, delta and gamma against S: (a) when the option is first written. (b ) shortly before time 71- Each graph should have three lines on it, one corresponding to the chooser option and one for each of its two components. [12] [Total 14]
