108156.pdf

130 Mathematics for Finance The formula can easily be generalised to the case when dividends are paid more than once: F(0,T)=[S( ...

Forward and Futures Contracts 131 Next, suppose that a stock pays dividends continuously at a raterdiv>0, called the (conti ...

132 Mathematics for Finance In general, if the contract is initiated at timet<T,then F(t, T)=S(t)e(r−rdiv)(T−t). (6.7) Exerci ...

Forward and Futures Contracts 133 Proof Suppose that V(t)<[F(t, T)−F(0,T)]e−r(T−t). If so, then at timet borrow the amount ...

134 Mathematics for Finance Such a contract may have non-zero value initially. In the case of a stock paying no dividends VX(0) ...

Forward and Futures Contracts 135 if positive, or will have to pay it if negative. The opposite payments apply for a short fut ...

136 Mathematics for Finance (positive numbers). n f(n, T) cash flow margin 1 payment margin 2 0 140 opening: 0 − 14 14 1 138 − 2 ...

Forward and Futures Contracts 137 Proof Suppose for simplicity that marking to market is performed at just two inter- mediate ...

138 Mathematics for Finance can be suitably modified and the equality between the futures and forward prices remains valid. In a ...

Forward and Futures Contracts 139 ‘m2m’ represents the payments due to marking to market and the last column shows the interes ...

140 Mathematics for Finance Example 6.3 Suppose we wish to sell stock after 2 months and we hedge using futures with delivery in ...

Forward and Futures Contracts 141 Going back to the problem of designing a hedge, suppose that we wish to sell an asset at tim ...

142 Mathematics for Finance multiplied by a fixed amount ($500 for futures on S&P500). If the number of stocks included in t ...

Forward and Futures Contracts 143 Proposition 6.6 If N=(βV−a)(1 +rF)V(0) f(0,T) , thenβV ̃=afor any given numbera. Proof We sh ...

144 Mathematics for Finance This means that the futures prices on the index (with delivery after 3 steps) are f(0,3) =M(0)(1 +rF ...

Forward and Futures Contracts 145 superior performance of the portfolio as compared to the market can be turned into a profit ...

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7. Options: General Properties................................ In Chapters 1 and 4 we have seen simple examples of call and put ...

148 Mathematics for Finance a European call option on the Standard and Poor Index (see page 141) with strike price 800 will gain ...

Options: General Properties 149 Exercise 7.1 Find the stock price on the exercise date for a European put option with strike p ...