**CppQuant Answer**

Delta = change in option price / change in underlying price, which can be approximated from the Black-Scholes-Merton formula as the value of N(d1) for calls and N(d1) - 1 for puts.

- d1 = ( ln(S0/X) + (r+stderr^2/2)*T) / (stderr*T^1/2) = ( ln(100/100) + (0.06 + 0.12/2)*1) / (0.1*1^(1/2)) = 0.65
- N(d1): In Excel, Normsdist(0.65) = 0.74
- For a $1 up(+) in the price of the stock, we expect the new call option price to be up(+) by 0.74.

*Bonus Points*

- The delta of a call option is always positive as the value of a call increases with an underlying price increase.
- The delta of a put option is always negative as the value of a put decreases with an underlying price increase.
- The put delta = N(d1) - 1 = 0.74 - 1 = -.026.
- For a $1 up (+) in the price of the stock, we expect the new put option price to be down(-) by 0.26.

- In general, the larger the move in the underlying price, the worse the approximation.

*Category: C++ Quant > Derivatives > Options*

**Elsewhere on BlogSpot**

Human Papillomavirus (HPV)

THE WELL-TIMED PERIOD - The highest rates of genital HPV infection are found in sexually active women younger than 25 ... Abstinence is not a risk free alternative (eg, here)...

Bush: Social Security Will be Bankrupt Because...

ECONOMIST S VIEW - ... the administration is suggesting workers invest in an account consisting of all Treasury bonds or notes that offers a negative risk-free rate of return...

Rich People Are Governments Best Friend

KUDLOW S MONEY POLITIC$ - That is why the unemployment rate has been averaging around 5 percent over the past 10 years ... Capitalism, free markts, reward for taking risk, ownership, ...

Replacement Level Yankees Weblog

INFORMATION PROCESSING - If you trade him, you risk the possibility that Soriano could improve, and become a Hall ... But, he does get on base at a good rate (because of his speed), ...

Michael Jackson Trial

KUDLOW S MONEY POLITIC$ - In scenes more reminiscent of a third rate Dracula movie, it appears that a ... 15-Days Risk-Free from FT.com! Click Here For The Wall Street Journal Online ...

## No comments:

## Post a Comment