Lecture 11: Financial Options

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Last updated 4:26 AM on 4/16/26
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14 Terms

1
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How do put & call options change with strike prices?

  • Call option (right to buy) value increases when strike price decreases → valuable when you pay less

Strike price (k) inc → Call value dec, Strike price (k) dec → call value inc

  • Put option (right to sell stock) value increases when strike price increases → can sell stock at higher price

Strike price (k) inc → put value inc, strike price (k) dec → put value dec

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How do put & call options change with stock prices?

  • Call option (right to buy) value increases when stock price increases → because can pay less

Stock price inc → call value inc, stock price dec → call value dec

  • Put option (right to sell) value increases when stock price decreases → because you can just sell the stock in the market

Stock price inc → put value dec, stock price dec → put value inc

3
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What are the 4 limits on option prices?

  1. American option can’t be worth less than European counterpart → American can be equally or more valuable

  2. Time value can’t be negative → can only add no value or positive value

  3. Call option can’t be worth more than stock itself → why buy call when can buy stock

C = (S - K, 0 otherwise)

  1. Put option can’t be worth more than strike price

P = (K - S, 0 otherwise)

4
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What is intrinsic value of an option (arbitrage opportunity)?

The value of option if option expired immediately right now

0 = out of the money

other than 0 = in the money

  • American option can’t be worth less than intrinsic value → otherwise, there’s an arbitrage opportunity if it is worth less!

5
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What is time value of an option?

Difference between option price & intrinsic value → can’t be negative

American price = intrinsic value + time value

  • option is more valuable when the exercise date is longer! (this is why American option is usually more valuable or equal to European)

6
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How are option prices related to volatility?

The value of an option increases with the volatility of the stock

  • lower volatility: expected return = 0 (worthless)

  • some volatility: option price has value (bc there is a possibility that payoff is $60)

<p>The value of an option increases with the volatility of the stock</p><ul><li><p>lower volatility: expected return = 0 (worthless)</p></li><li><p>some volatility: option price has value (bc there is a possibility that payoff is $60)</p></li></ul><p></p>
7
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How can call parity without dividends be split into intrinsic & time value?

  • Never valuable/optimal to exercise non-dividend call option early! → bc price of any call option always exceeds intrinsic value (price is more than the value you get)

  • European call always has a positive time value bc you can only exercise on expiration date

  • Negative discount(k) means option can be negative at time value → happens when deep in the money & K is very large (better to buy early than sell in market if deep in the money!)

<ul><li><p>Never valuable/optimal to exercise non-dividend call option early! → bc price of any call option always exceeds intrinsic value (price is more than the value you get)</p></li><li><p>European call always has a positive time value bc you can only exercise on expiration date</p></li><li><p>Negative discount(k) means option can be negative at time value → happens when deep in the money &amp; K is very large (better to buy early than sell in market if deep in the money!)</p></li></ul><p></p>
8
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When do you sell or exercise a call option?

Sell → if price is higher than payoff

Exercise → if price is less than payoff

  • Same for with & without dividends!

<p>Sell → if price is higher than payoff</p><p>Exercise → if price is less than payoff</p><ul><li><p>Same for with &amp; without dividends!</p></li></ul><p></p>
9
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When do you sell or exercise a put option without dividends?

Sell → if price is higher than payoff

Exercise → if price is less than payoff

  • Same for with & without dividends!

<p>Sell → if price is higher than payoff</p><p>Exercise → if price is less than payoff</p><ul><li><p>Same for with &amp; without dividends!</p></li></ul><p></p>
10
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What is the call parity with dividends split into intrinsic & time value?

  • If time value is negative, better to exercise early! → bc you can capture the dividend itself

  • If PV(Dividend) is large enough, price can be less than intrinsic value → can’t happen bc arbitrage opportunity

* Sometimes better to exercise early with dividends, never better to exercise early without dividends!

<ul><li><p>If time value is negative, better to exercise early! → bc you can capture the dividend itself</p></li><li><p>If PV(Dividend) is large enough, price can be less than intrinsic value → can’t happen bc arbitrage opportunity</p></li></ul><p><strong>* Sometimes better to exercise early with dividends, never better to exercise early without dividends!</strong></p><p></p>
11
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How is call option value related to debt?

  • When firm value goes down (can’t pay debt) → call option is worthless

  • After company repays debt, the remaining goes to equity holders/shareholders

D → debt is a fixed amount

A → value of firm asset

If asset less than debt → worthless

If asset = debt → worthless

If asset more than debt → payoff id Asset - Debt

<ul><li><p>When firm value goes down (can’t pay debt) → call option is worthless</p></li><li><p>After company repays debt, the remaining goes to equity holders/shareholders</p></li></ul><p>D → debt is a fixed amount</p><p>A → value of firm asset</p><p>If asset less than debt → worthless</p><p>If asset = debt → worthless</p><p>If asset more than debt → payoff id Asset - Debt</p><p></p>
12
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What is debt as an option portfolio?

Debt holders → owner of firm
Owners → sell call option to equity holders

Call option strike price = debt outstanding

<p>Debt holders → owner of firm<br>Owners → sell call option to equity holders</p><p>Call option strike price = debt outstanding</p>
13
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What is risky debt?

Risky debt = Risk-free debt - put option on firm assets

  • when firm assets are worth less than required debt payment, owner of put option will exercise & receive difference between required debt payment & asset value

  • If firm value is greater than required debt payment, debt holder only receives required debt payment

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How can you get risk-free debt?

By rearranging risky debt

  • Credit default swap → buyer pays premium to seller & receives payment from seller to make up for loss

<p>By rearranging risky debt</p><ul><li><p>Credit default swap → buyer pays premium to seller &amp; receives payment from seller to make up for loss</p></li></ul><p></p>