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Created 7/1/1996
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Business Administration 130:

Options I

http://www.j-bradford-delong.net/Intro_Finance/BAonethirty20.html


Basics:

 


Interactions of Investment and Financing:


Options:


Calls, Puts, and Shares:

Intel Options Prices in July 1995; Stock Trading at $65 a Share

 Exercise Date

Exercise Price

Price of Put

Price of Call

 10/95

$65

$6.25

$4.625

1/96

$65

$8

$5.875

1/96

$70

$5.875

$8.5

Value of call at expiration = max(price of share - exercise price, 0)

Value of put at expiration = max(exercise price - price of share, 0)

Bachelier diagrams//payoffs to owners/payoffs to writers

[buy call, invest PV of exercise price in safe asset] has the same payoff as [buy put, buy share]

V[call] + PV[exercise price] = V[put]+[share price]

[buy call, sell put] has the same payoff as [buy share, borrow PV of exercise price]

Synthetic Option:

Buy put = buy call + sell share + invest PV of exercise price

Bankruptcy as shareholders' exercise of a put option


What determines option values?

Value of call is less than share price; value of call is greater than payoff if exercised immediately


Why DCF Doesn't Work for Options:

Because the riskiness of an option changes every time the stock price moves.


Valuing Options:

Price options by constructing a synthetic option.

Suppose we have our $65 Intel stock, and buy a call option with a strike price of $65 and an expiration date six months from now. r of 5% per year. If Intel stock can only (a) fall by 20% to $52 or rise by 25% to $81.25, then

Option value = 0 in bad case; $16.25 in good case. Spread=5/9 spread of stock price. Suppose you bought 5/9 of a share and borrowed the PV of 5/9 of a share in the bad case from the bank--borrow $28.18, the PV of $28.89.

Then you have the same payoffs as the option. Value of 5/9 of a share today is $36.11, minus $28.18 = $7.93. We have just valued our option. The number of shares to replicate the spread from an option is the hedge ratio or option delta. (If the option sells for more than $7.93, you have a money machine by selling options and covering.

Value of put option--option delta = -4/9; payoff = +$13 in low state; = 0 in high state; sell 4/9 of a share and lend out $35.23 (collect $36.11 in six months). $35.23 - 4/9 x $65 = $6.34.

V[call] + PV[exercise price] = V[put]+[share price]

$7.93 +$65/1.025 = $6.34 + $65


Summary:

Our authors have gotten punchy....

Black-Scholes

 


Adam Smith
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