108156.pdf

190 Mathematics for Finance Rather than looking at the details of this limit, we just refer to Figure 8.2 for illustration. It s ...

9. Financial Engineering....................................... This chapter shows some applications of derivative securities to ...

192 Mathematics for Finance 9.1 Hedging Option Positions.................................. The writer of a European call option ...

Financial Engineering 193 written, that is,z=−1. Then d dS V(S)=x− d dS D(S). The last termddSD(S), which is thedeltaof the de ...

194 Mathematics for Finance withd 2 is given by (8.9). Let us analyse the following example, which will subsequently be expanded ...

Financial Engineering 195 3. The stock price goes down toS( 3651 ) = 59 dollars. The value of the written options decreases, a ...

196 Mathematics for Finance Now, let us see what happens if the stock price changes are considerable: S V U 50 − 2 , 233. 19 3 , ...

Financial Engineering 197 As we can see, in some circumstances delta hedging may be far from satis- factory. We need to improv ...

198 Mathematics for Finance we should design a portfolio with both delta and vega equal to zero (delta- vega neutral). Adelta-ga ...

Financial Engineering 199 9.1.3 Applications ....................................... To show some possibilities offered by Gre ...

200 Mathematics for Finance day. The values of the portfolio are given below (for comparison we also recall the values of the de ...

Financial Engineering 201 Suppose that the volatility increases toσ= 32% on day one. Let us compare the results for delta-vega ...

202 Mathematics for Finance 9.2.1 Value at Risk ...................................... Let us present the basic idea using a sim ...

Financial Engineering 203 Exercise 9.9 Suppose that $1,000 is invested in European call options on a stock with current priceS ...

204 Mathematics for Finance pounds): sales 5 , 000 , 000 cost of sales − 3 , 000 , 000 earnings before tax 2 , 000 , 000 tax − 4 ...

Financial Engineering 205 As a result, VaR∼= 431 ,818 dollars. The final balance as a function of the exchange ratedis b(d) = ...

206 Mathematics for Finance disappointing: sales 5 , 000 , 000 cost of sales − 3 , 000 , 000 earnings before interest and tax 2 ...

Financial Engineering 207 5.Combination of Options and Forward Contracts.Finally, let us inves- tigate what happens if the com ...

208 Mathematics for Finance 9.3 Speculating with Derivatives............................... 9.3.1 Tools ........................ ...

Financial Engineering 209 shows the case whenX′′is the average of the other two strike prices.Reversed butterflyis the opposit ...