中南财大金融经济学课件 第六章

1. Options (1) Call options and put options A call option gives the holder the right to buy the underlying asset by a certain date (expiration date) for a certain price (strike price or exercise price). A put option gives the holder the right to sell the underlying asset by a certain date for a certain price. Options: right, not liability
Invest
in the riskless asset and buy the futures.
,
,
,
.
Risk of the underlying asset risk of the investment
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6.2 Valuation of options
2. Option price: the cost to acquiring an option
(1) The purchaser: Buy the option, cost = option price
Have the right to buy or sell the underlying asset by a certain date
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Ch6 Valuation of Derivatives
6.1 Valuation of Futures
1. Derivative security: a financial instrument whose value depends on other more basic underlying assets. 2. Futures: agreement to buy or sell an asset at a certain time in the future for a certain price. Futures price and spot price
Payoff:
,0 , Profit:
(4) Short position in a put option
payoff: 0
payoff:
Payoff:
,0 , Profit:
,0) ,0)
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4. Upper bounds for option prices (European options)
Investment
Return
, an arbitrage
No arbitrage
.
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5. Futures price when the underlying asset provides an income at time ( ) Method 1: purchase the underlying asset and short the futures.
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, no arbitrage
,
.
(2) With dividends:
.
7. Early exercise on American options
(1) American call option on a non-dividend-paying stock should
never be exercised early.
,
if
not to exercise the option,
,
if
to exercise the option,
,
.
Portfolio B: cash
,
, no arbitrage
, and
.
(4) European put option on a stock with dividends
.
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. riskless rate, riskless rate in the foreign country
Method 1: invest at home:
.
Method 2: invest in the foreign country and short the foreign
currency (not )
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3. Continuous compounding (1) Simple interest rate: (2) Compound interest rate: (3) Continuous compounding The number of compounding periods every year: ,
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6. Put-call parity (European options)
(1) Without dividends
Portfolio A: one European call option + cash
,
if
to exercise the option,
.
.
No arbitrage
.
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7. Relationship between futures price and expected future spot price
.
Expected future spot price
,
Investment :
, .
, Method 2: invest at riskless rate
, No arbitrage: same investment, same risk same return.
. .
present value of
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6. Foreign currencies futures spot exchange rate: the current spot price of foreign currency forward exchange rate: the forward price of foreign currency
.
,
.
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4. Futures price when the underlying asset doesn’t provide any
income.
: futures price, : spot price, : maturity date, riskless rate
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(2) American options and European options
American options can be exercised at any time up to the expiration
date.
European options can be exercised only on the expiration date.
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5. Lower bounds for option prices (European optil option on a non-dividend-paying stock
.
Portfolio A: one European call option + cash
,
if
not to exercise the option,
,
.
Portfolio B: one European put option + one share
,
if
not to exercise the option,
,
if
to exercise the option,
,
.
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Financial Economics
If
sell the option and invest in riskless asset, investment
if
the holder will give up the right,
if
the holder will exercise the option,
.
, .
.
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,
if
to exercise the option,
,
if
not to exercise the option,
,
.
Portfolio B: one share
,
, no arbitrage
, and
.
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Financial Economics
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(2) European call option on a stock with dividends.