Lecture 15-Fin4710

Cons fo BSM

Limitations•Derived for European calls and stocks do not pay dividends•Could adapt to incorporate dividend payments•For put options, use put-call parity to derive the values•American options are AT LEAST as valuable as comparable European options•Serve as a lower bound of American option values•Need other assumption about stock return distributions and those could beviolated in reallife situation IDK

difference between payoff and profit

payoff is the amount you would receive from exercising the option at expiration,

profit is payoff minus premium for a call and put

risk-neutral probability

changing the probability of different states that we can borrow the risk-neutral pricing methods IDK

Theta

Time to expiration

(Delta) Represented by S

Underlying asset price •

Number of shares we’re investing in the stock

Volatility change

(Vega)

Rho

•Underlying risk-free rate (

Gamma

Measures how Delta changes with respect to underlying asset value

Delta Hedging

is like tying a balloon to a string and adjusting the string based on how strong the wind is to keep the balloon steady. In finance, it means balancing your investments by counteracting the price sensitivity (delta) of an option through trades in the underlying asset, which is the stock or security the option is based on. For example, if you own an option, you might buy or sell shares of the stock to reduce the risk of losing money when the stock price changes. By constantly adjusting the hedge as delta changes, you ensure your portfolio stays stable despite market movements.