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174MT2Conceptsheet

# 174MT2Conceptsheet - Concept Study Sheet Midterm II Math...

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Concept Study Sheet Midterm II Math 174 Winter 2011 On examinations you are responsible for the content of readings, lectures and homework. Use this guide to help you study the topics. It is more effective to study explicitly topic by topic than to just reread the text. Overview: we studied Chapters 11,12, 13, also reviewing in lecture some basic probability concepts, esp. pertaining to the normal distribution. since the last midterm. You will be tested this content. The overall main topic is derivative pricing. As last time, it is worthwhile to recall that many finance and probability concepts have very good wikipedia articles on them; I recommend that you use this and other web resources as you need them. Chapter 11. One step binomial model. Be able to set up and solve a problem with numbers. Be able to find the portfolio (stock plus cash invested or borrowed at rate r) that replicates a given derivative. Be able to find the portfolio of stock and cash that is risk free. (See below about Delta.) Be able to find the risk neutral measure. Be able to derive and implement formulas 11.1-11.3. Be able to explain why the actual probability of u and d moves is irrelevant to the price of the option. Make sure you understand how the pricing theory is built on the principle of no arbitrage. Be able to explain to show that in a risk neutral world (one where the risk neutral measure gives the probability of u and d moves), the expected value of the stock is given by 11.4. Be able to compute risk neutral probability of p (of an up move) using this formula (i.e. by risk neutral valuation). Be able to compute with multiple step trees, and derive formulas 11.7-11.10, and their generalizations to multiple steps. Be able to use binomial method to price puts and calls. Be able to price American calls where at each node n you exercise early iff the value f_n of the option at that node n is less than the payoff gotten from early exercise. Exercise: be able to show in the one-step case that it is never optimal to early exercise an American call. Show that this is not so for a put. Understand the quantity delta given by 11.1, i.e. it is the number of shares of stock to hold for each option shorted, in order for the resulting portfolio to be riskless. Be able to start from a given volatility sigma and compute the Cox-Ross-Rubinstein values for u and d (and hence p) using 11.13-11.16.

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174MT2Conceptsheet - Concept Study Sheet Midterm II Math...

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