Errata: Known Errors in "Basic Black-Scholes" |

- No known errors discovered yet.

- Footnote 19 on page 34 says F<=Se^(c(T-t)) for consumption commodities. This is correct if c is the cost of carry *without* the convenience yield but incorrect otherwise. Let r=interest rate, s=storage costs, q=dividend yield (zero here), and y=convenience yield. Then the footnote should say F=Se^((r+s-y)((T-t))<=Se^((r+s)(T-t)). I thank Jerome Healy for finding this error.
- On page 49, Restriction R8 contains a typo. "(C, or c)" should just be "C". R8 applies only to American-style options. I thank a reader for finding this error. Note that Restriction R3c shows the biting effect of dividends. A deep-in-the-money European-style call can easily be worth less than S-X if the dividend yield is high enough. You can bump up the dividends in bbsGREEKS.xls (download from the main page) to see the European call price quickly dropping below S-X for deep-in-the-money calls.
- There is a careless mistake in Footnote 5 on page 3. The words "As a US immigrant from Europe..." should be replaced by "As a US economist..." The story is correct, but the preamble is wrong.

- There is a careless mistake in Footnote 4 on page 4. The words "As a US immigrant from Europe..." should be replaced by "As a US economist..."
- Footnote 19 on page 40 says F<=Se^(c(T-t)) for consumption commodities. This is correct if c is the cost of carry *without* the convenience yield but incorrect otherwise. Let r=interest rate, s=storage costs, q=dividend yield (zero here), and y=convenience yield. Then the footnote should say F=Se^((r+s-y)((T-t))<=Se^((r+s)(T-t)).
- The HP12C code in Table A.3 is correct, but I fail to tell the reader that if you have an HP12C Platinum you need to enter an extra 0 in Lines 71, 79, and 88. That is, for example, Line 71 becomes: g GTO 077 (because the 12C Platinum uses three digits for line numbers). Otherwise, the code is fine, although the screen display differs slightly because of the new placement of some keys on the 12C Platinum. My code is in RPN, so you have to have the machine in RPN, not ALG, before entering the code.
- On page 157 in the box there are two errors. First, in the third equation from the top, the minus sign in the exponent of the discounting term should be a plus. That is, the formula should read E^*[S(T)|S(T) less than X] = e^{+r(T-t)}S(t)N(-d1)/N(-d2). Second, in the OP Quiz, my answer is no, but a reader has pointed out that the answer is in fact yes! He has supplied the following formulae (which look very good to my eye but which I have not yet checked in detail): c=S0[1-X*Ebar[1/S(T)|S(T)>X]]N(d1) and p=S0[X*Ebar[1/S(T)|S(T)>X]-1]N(-d1), where "Ebar" is the expectation taken with respect to the stock-numeraire equivalent martingale measure. These results are really nice and do follow from all the previous material. My experience has been that many people do not understand risk-neutral pricing. Having this alternative equivalent martingale measure decomposition to compare with and contrast to should help.
- On page 190, m=(r+(1/2)sigma^2)*(alpha-1) should read m=(r+(alpha/2)sigma^2)*(alpha-1).
- On page 196 I say "The jumps occur just infrequently enough that on average, they balance the excess returns on the Black-Scholes hedge; and on average, the hedge returns zero." I say this in the context of the general jump diffusion, but in fact, it is not true at all. In the case of the jump with diversifiable jump risk, the equilibrium return on the hedge is the riskless rate. In the non-diversifiable jump case, the return when there is a jump does balance the return during normal time to some extent, but not well enough to make the equilibium return on the hedge equal to the riskless rate; the hedge is risky.

Back to Main Page