Financial Modelling 2557A/B Chapter 5: Chapter 5

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Financial Modelling
Course Code
Financial Modelling 2557A/B
Xiaoming Liu

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Outright Purchase: The typial way to think about buying stock - simultaneously purchasing of stock in cash and receiving ownership of stock Fully Leveraged Purchase: Borrowing the entire purchase price for the security to purchase and recieve it now but pay for it later rt  The amount owed at time T = S e ,0where r = continuously compounded interest rate Prepaid Forward Contract: Agreement in which you pay for the stock today and receive the stock at an agreed upon future date  Unlike outright purchase, you receive it at time T, so the price you pay is not necessarily the stock price Forward Contract: An agreement in which you both pay for the stock and receive it at a specified time T Prepaid Forward Contract A prepaid foreign contract entails paying today to receive something in the future  The sale of a prepaid forward contract permits the owner to sell an asset while retaining physical possession for a period of time By delaying physical possession of the stock, you do not receive dividends and have no voting/control rights When there are no dividends, the price of the prepaid forward contract is the stock price today FP = S 0,T 0 Arbitrage: A situation in which we can generate a positive cash flow either today or in the future by simultaneously buying and selling related assets, with no net investment of funds and with no risk  Free money  The price of a derivative should be such that no arbitrage is possible When a stock pays a dividend, the prepaid forward price < the stock price  Owner of stock receives dividends, but owner of prepaid forward contract does not o Prepaid forward price must be adjusted to reflect dividends received by the shareholder and not by the owner of prepaid forward contract 2 types of dividends: 1. Discrete o FP0,T S 0 Reimann{i=1 to n}(PV(Dividends)) o Assumes dividends are certain 2. Continuous o Rate proportional to the level of the index - the dividend yield Is constant o Approximation o Dividend yield not likely to be fixed in short run: if prices rise, yield falls temporarily o Assume constant proportional dividend yield delta*t o Because of dividend reinvestment, at time T, we have e more shares than we started with  Tailing: Adjusting initial quantity to offset the effect of income from the asset P -delta*t o F 0,T S 0 Forward Contracts on Stock If we know the prepaid forward price, we can compute the forward price  Difference between prepaid forward contract and a forward contract is the timing of the payent for the stock o Immediate for prepaid, deferred with forward o Forward contract initially costless for buyer and seller F0,TFV(F P0,T = e S0e -delt=e(r-dS*0  In this case, r=yield to maturity for default-free zero coupon bond with the same time to maturity as the forward contract Forward Premium: Ratio of the forward price to the spot price Fair Value: Asset price implied by forward pricing formulas defines fair value for underlying stock or index The forward price = expe
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