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Finance (Subject) / Options (Lesson)
- Options Call options: the right, but not the obligation, to buy a share of stock at a given price Put Options: the right, but not the obligation, to sell a share of stock at a given price Underlying asset: Usually equity, could be a bond, an interest rate or a currency Exercise price/Strike price: Price at which the financial security can be bought or sold Expiration date/Maturity date: date on which the option expires Exercise style: when can you exercise your option? European (on expiration date) vs. American (any time) - American option can not be less valuable than its Europeancounterpart. (Why?)
- Call Option Long Call: Max [ ST −X , 0 ] Short Call: - Max [ ST −X ; 0 ] = Min [ 0, X −ST ] When you are long and wrong, risk is limited. Selling Call Options can be very expensive When you are short and wrong, you can theoretically lose an indefinite amount.
- Put Option Buy A Put: max(K-ST,0) Sell A Put: -max(K-ST,0) = Min (0,ST −X)
- Why do we need options? Directional bets are cheaper than buying stock- If you think the stock price is going up, why not just buy a call instead of the stock?- If you think the stock price is falling, why not just buy a put instead of shorting? Currently hold stock and want to lock in payoffs: protective put - Long a Stock (restricted Stock) - Long a Put with same Maturity - If Stock ends above 25, the put option expires out of the money. - If Stock ends below 25, the Option will pay and losses are minimized
- The Merton Model price risky bond = price riskfree bond - put option price Gold Inc (50m enterprise Value) has one zero coupon bond outstanding that matures in one year The face value of the ZCB is £40m Depending on the price of gold Gold Inc may be worth more or less in one year As long as Gold Inc’s gold is worth at least £40m when the bond payment is due, bondholders get all their £40m ...but if the value of Gold Inc has dipped below £40m then Gold Inc cannot repay! Payoff to Debtholers = K - max (K-VT,0) = K - max(£40m - Enterprise Value,0) We can decompose K −max(K −VT ,0) into two components 1) Getting K is like owning a risk-free ZCB with face Value K 2) Paying -max(K-VT,0) is like selling a put option with strike Price K on Enterprise Value
- Real Options - To delay an investment on a project- To adjust capacity if demand shrinks or increases - To exploit the follow-on opportunities presented by a project Value of flexibility is never negative Value of the Option = Total NPV - Static NPV* *Static NPV of the project if there is no option not to activate plant one year from now
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