PRINCIPLES OF OPTION PRICING
END-OF-CHAPTER QUESTIONS AND PROBLEMS
The average of the bid and ask discounts is 8.22.
Discount = 8.22(68/360) = 1.5527
Price = 100 - 1.5527 = 98.4473
Yield = (100/98.4473)
- 1 = .0876
Note that even though the T-bill matured in 67 days, we must use 68 days since that is the option's time to
This would create an arbitrage opportunity.
The call would be purchased and immediately exercised.
example, suppose S = 44, E = 40, and the call price is $3.
Then an investor would buy the call and
immediately exercise it.
This would cost $3 for the call and $40 for the stock.
Then the stock would be
immediately sold for $44, netting a risk-free profit of $1.
In other words, the investor could obtain a $44 stock
Since everyone would do this, it would drive the price of the call up to at least $4.
If the call were
European, however, immediate exercise would not be possible (unless, of course, it was the expiration day), so
the European call could technically sell for less than the intrinsic value of the American call.
We saw, though,
that the European call has a lower bound of the stock price minus the present value of the exercise price
(assuming no dividends).
Since this is greater than the intrinsic value, the European call would sell for more
than the intrinsic value.
Then at expiration, it would sell for the intrinsic value.
European call: We know that its price cannot exceed S but must exceed Max(0, S-E(1+r)
With an infinite
time to expiration, the present value of E is zero so the lower bound is S and, since the upper bound is S, the
call price must be S.
American call: We know that its price cannot exceed S but it must be at least as valuable as a European call.
Thus its value must also be S.
Note that if exercised early it would be worth only S-E so it will never be
Ordinarily the option with the longer time to expiration would sell for more.
If both options were deep out-of-
the-money, however, they could both sell for essentially nothing.
The market would be expecting that both the
shorter- and longer-lived options will expire out-of-the-money.
If both options were deep out-of-the-money, they might have prices of zero.
As in the previous question, the
two options are expected to expire out-of-the-money.
The call is underpriced, so buy the call, sell short the stock, and buy risk-free bonds with face value of E. The
cash received from the stock is greater than the cost of the call and bonds.
Thus, there is a positive cash flow
The payoffs from the portfolio at expiration are as follows:
(from the stock)
(from the bonds)
the total, E - S
, is positive
(from the call)