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1、CHAPTER 7 the BlackScholes formulae and the greeksIn this Chapter the derivation of the BlackScholes formulae for calls, puts and simple digitals the meaning and importance of the greeks, delta, gamma, theta, vega and rho the difference between differentiation with respect to variables and to parame
2、ters formulae for the greeks for calls, puts and simple digitalsthe derivation of the BlackScholes formulae for calls, puts and simple digitals: （Omitted略）When the asset is at-the-money forward, i.e. then there is a simple approximation for the call value (Brenner this procedure is called dynamic he
3、dging. Changing the number of assets held requires the continual purchase and/or sale of the stock. This is called rehedging or rebalancing the portfolio. Gamma: The gamma of an option or a portfolio of options is the second derivative of the position with respect to the underlying: Theta: Theta is
4、the rate of change of the option price with time: Vega: Vega, a.k.a. zeta and kappa, is the sensitivity of the option price to volatility: Rho: Rho, , is the sensitivity of the option value to the interest rate used in the Black Scholes formulae:IMPLIED VOLATILITY If we can see the price at which th
5、e option is trading, we can ask What volatility must I use to get the correct market price? This is called the implied volatility. The implied volatility is the volatility of the underlying which when substituted into the BlackScholes formula gives a theoretical price equal to the market price.A CLA
6、SSIFICATION OF HEDGING TYPESWhy hedging? Hedging in its broadest sense means the reduction of risk by exploiting relationships or correlation between various risky investments (or bets). The concept is used widely in horse racing, other sports betting and, of course, high finance. The reason for hed
7、ging is that it can lead to an improved risk/return.The Two Main Classifications:Model-independent hedging; Model-dependent hedging.Other Classifications:delta hedging; gamma ; Vega hedging Static hedging Margin hedging Crash /platinum hedging 练习题1: 宝钢股份的看涨期权相关资料如下:欧式还 有0.5年到期,执行价格为3元,无风险利率为 5%,宝钢股价现在为4元;假设宝钢股份无分 红;宝钢股价收益率的波动率为20%,计算该 看涨期权的价值，并计算五个希腊字母。 练习题2: 宝钢股份的看跌期权相关资料如下:欧式还 有0.5年到期,执行价格为5元,无风险利率为 5%,宝钢股价现在为4元;假设宝钢股份无分 红;宝钢股价收益率的波动率为20%,计算该 看跌期权的价值，并计算五个希腊字母。
