what is a call option?
A call option on a financial asset gives the holder the RIGHT, but NOT the OBLIGATION, to buy a certain quantity of an underlying asset [S] (e.g. shares) at a fixed price [K] (called the strike price or “exercise price”) during
the exercise period (American option) or at the future expiration date (European option) of the option.
what is the profit of an option?
value of the underlying asset (S) - exercise price (K)
why is the value of european options always lower than the value of American options (all else equal)?
european options can only be exercised at EXPIRATION, the right to exercise is LIMITED
what are the 4 characteristics of an option?
- it is discretionary (execution is not mandatory). In a LIMITED liability regime, the shareholder CAN DECIDE to repay maturing DEBT or not and let the company go bankrupt
- it can be exercised at a future time [T]. IF the debt is ON DEMAND (possibility of INSTANT REIMBURSEMENT), the option would have no value
- it can be exercised under PREDEFINED CONDITIONS [K] (IF debt is SUBJECT to NEGOTIATION, as in restructuring, then it is not possible to determine the value of the option WITHOUT making HYPOTHESES on the possible values)
- it DEPENDS on the occurrence of an EXTERNAL VARIABLE that is UNCERTAIN [stdv]
!!! however the probability distribution is known
what is the value of an option? what does it depend on (6 variables)?
!!!!CALL OPTION!!!!
the value of an option depends on the probability that the stock price at expiration is higher than the exercise price and on the difference between S and K. The VALUE is equal to the EXPECTED VALUE DIFFERENCE between
(discounted) S and (discounted) K
the 6 variables affecting the value of a call option:
- underlying S (+)
- exercise price K (-)
- volatility (+)
!!!! owner of an option benefits from upward risk but is protected against downside risk, by being able to not exercise the option !!!! - risk free (+): the present value of K decreases as the discount rate increases
- Duration (+): GREATER VOLATILITY and GREATER DISCOUNT of K (exercise price)
- ** dividends** (-)
!!!! when a stock pays a dividend, the market price is adjusted to reflect the dividend paid (decreases)
why can a company’s equity be seen as an option?
equity is a “residual claim”
shareholders can claim the right to all cash flows generated by the company after other holders of financial and operating claims have been satisfied. Furthermore, in LIMITED LIABILITY regimes shareholders actually have the OPTION to
1. repay debt and maintain ownership
2. not repay debt and give all assets to debtholders
!!!! this principle applies to both going concern and liquidated scenarios
what is the assumption behind debt in “equity as an option”?
debt is represented by a single issue of zero coupon bonds with a fixed duration, and the life of the equity as a call option corresponds to the duration of the bond.
5 precautions in applying the option valuation model to companies
(especially unlisted ones)
- underlying asset may NOT be TRADED on the market
- PRICE of the asset may NOT follow a CONTINUOUS process. Black and Scholes model assumes there are no “price jumps”, the assumption may be violated especially for unlisted companies
- variance may NOT be KNOWN or CHANGE during the life of the option
- exercise may NOT be INSTANTANEOUS (buy/sell instantly)
- returns on S may not follow a NORMAL distribution (applies to both listed and, especially, unlisted companies)
does option theory apply when debt is “at sight” (no maturity)?
NO
in fact, as soon as EV=D the debtholders request an immediate payment in order to not fall into a loss condition
does option theory apply when volatility is 0?
NO
no one would pay a premium if they knew a priori what the certain value would be at time T
all other things equal is the equity of a company with more volatile operating returns worth more according to option theORY?
YES
if the difference between initial EV and D_nom is very small, what happens to value of equity as an option?
equity is worth a lot in relative terms since shareholders still have the possibility of achieving high prices
what is the advantage of the option approach with respect to the traditional approach?
equity as an option approach can be seen as a composition of two values:
1. the value according to the traditional approach E = EV-D
- the value of “strategic change” in the economic conditions of the firm, considering risk and time
black & scholes model formula
.
B&S exercises
from slide 23 onwards
