MSc IN MATHEMATICAL TRADING AND FINANCE;DERIVATIVES 2 (SMM615)/Dversities.

The coursework aims to test your understanding and intuition. Make sure that
your answers are as detailed and complete as possible. make explicit assumptions
where you think is necessary. This is not a coursework to test primarily your com-
putational skills by producing a solid code, rather an exercise in solving ?nancial
issues; therefore the platform will be Excel.
You are asked to build a Derman and Kani- type (binomial ) implied arbitrage-
free volatility tree. The number of periods will be ?ve. You may use options on
any asset class, as long as they are liquid (options on stock market indices such as
S&P 500 are quite suitable) for any period from 2010 onwards. Make sure that you
take care of dividends ( if applicable), early optionality (eg., American options,
if applicable). Provide details of the interpolation/extrapolation methods to con-
struct the input option/implied volatility data. Make explicit assumptions about
centering the tree and construct also the implicit Arrow-Debreu tree. Discuss how
you handle “bad probabilities”, i.e., violations of the no-arbitrage condition.
As a baseline, you should construct a similar constant volatility binomial tree
(for example, Cox-Ross-Rubinstein). Calculate the “Greeks” and compare them
with your ?ndings from the implied volatility tree. Discuss your ?ndings.