Assignment 1: Risk Neutral Valuation
Market Consistent (MC) ESG simulations can be used to calculate the value of financial derivatives today. This value will depend on the evolution of financial risk drivers (e.g. interest rates, equity prices) which are modelled stochastically within the ESG.
For this exercise you should set up an MC simulation in the ESG to model the GBP economy over 10,000 trials with the following model choices:
– E(D)2FBK model for nominal interest rates.
– SVJD model for equity assets.
– EndDec2018_MC_GOVT_Global_Standard_SVJD.bhc calibration file.
A wealthy investor holds a portfolio of UK securities and derivatives that all mature in 10 years¡¯ time. This portfolio consists of:
– 10 year European put option on UK Equity with a strike of ¡ê4,000. – 10 year European call option on UK Equity with a strike of ¡ê6,000. – Zero coupon government bond paying ¡ê8,000 in 10 years¡¯ time.
If the underlying UK Equity has a current market value of ¡ê5000 then:
i) Plot the payoff structure of the wealthy investor¡¯s portfolio.
ii) Calculate the market consistent value of the portfolio.
iii) Estimate the 95% confidence interval for the value of the portfolio.
The wealthy investor has decided to leave some inheritance to his two children; a son and a daughter. One of them will inherit the whole portfolio. In particular,
– The daughter will inherit the portfolio if UK Equity ¡Ý ¡ê5,000 – The son will inherit the portfolio if UK Equity < ¡ê5,000
The portfolio proceeds are only distributed after 10 years.
iv) Plot the payoff structure for each child¡¯s inheritance.
v) Calculate the market consistent value of each child¡¯s inheritance.
vi) Outlineanyweaknessofthisvaluation.
vii) Write a report or prepare a 20 minute presentation detailing the calculation of the market
consistent value of the portfolio.