a***r
发帖数: 146 | 1 Today's price is $110 tomorrow could be 110, 100 or 0
interest rate=0
can we price the call option with $100 striking price?
what if tomorrow could be 110(99% chance), 100(0.5%) or 0(0.5%)
can we price the option? | f******y
发帖数: 2971 | 2 nobody want to answer this one?
I think both of them are $10. | p******i
发帖数: 1358 | | p*****k
发帖数: 318 | 4 finalguy, $10 would be the upper bound. note unless
it's doomed to be $110, something worth at most $10 tmr
cannot be $10 today (with the interest rate=0)
it's an incomplete market, so you could only get a price
range due to different risk-neutral measures. since the
final payoff is either 10 or 0, the range of the price is
simply [0,10]
i guess for (2), due to the equivalent measure constraint,
one gets (0,10) | b***k
发帖数: 2673 | 5 should it be in a range of [0,5]?
【在 p*****k 的大作中提到】
: finalguy, $10 would be the upper bound. note unless
: it's doomed to be $110, something worth at most $10 tmr
: cannot be $10 today (with the interest rate=0)
: it's an incomplete market, so you could only get a price
: range due to different risk-neutral measures. since the
: final payoff is either 10 or 0, the range of the price is
: simply [0,10]
: i guess for (2), due to the equivalent measure constraint,
: one gets (0,10)
| j****i
发帖数: 305 | 6 Why it's an incomplete market? Could you explain your thoughts in detail?
【在 p*****k 的大作中提到】
: finalguy, $10 would be the upper bound. note unless
: it's doomed to be $110, something worth at most $10 tmr
: cannot be $10 today (with the interest rate=0)
: it's an incomplete market, so you could only get a price
: range due to different risk-neutral measures. since the
: final payoff is either 10 or 0, the range of the price is
: simply [0,10]
: i guess for (2), due to the equivalent measure constraint,
: one gets (0,10)
| s*******u
发帖数: 35 | 7 The risk neutral measure is unique in this situation: 110 with prob 1 and
others 0; So we can price it.
【在 a***r 的大作中提到】
: Today's price is $110 tomorrow could be 110, 100 or 0
: interest rate=0
: can we price the call option with $100 striking price?
: what if tomorrow could be 110(99% chance), 100(0.5%) or 0(0.5%)
: can we price the option?
| r******o
发帖数: 1530 | 8 can't price it, you have more states ( 3 ) than the number of securities ( 2
), you can't replicate the option, need a third asset in order to do that. | p*****k
发帖数: 318 | 9 sorry, had been posting things nonsensical late last night:P
the price range should be [0,100/11].
the risk neutral measure gives:
110*p1+100*p2+0*p3=100 (stock price would be martingale)
p1+p2+p3=1,
hence p3=p1/10 and p2=1-11/10*p1, which results the bound
0<=p1<=10/11.
then note the call price is (110-100)*p1+0*(p2+p3)=10*p1
with the given physical prob, then p1 or p2 cannot be 0
due to the equivalence of the prob measures, so (0,100/11) | s*******u
发帖数: 35 | 10 pcasnik, if today's price is 100, you are right. but here the price is 110
to start from. So we actually have p1=1, p2=p3=0. Of course, this stock
does not make too much sense. But purely from pricing point of view, this
means we can price it.
【在 p*****k 的大作中提到】
: sorry, had been posting things nonsensical late last night:P
: the price range should be [0,100/11].
: the risk neutral measure gives:
: 110*p1+100*p2+0*p3=100 (stock price would be martingale)
: p1+p2+p3=1,
: hence p3=p1/10 and p2=1-11/10*p1, which results the bound
: 0<=p1<=10/11.
: then note the call price is (110-100)*p1+0*(p2+p3)=10*p1
: with the given physical prob, then p1 or p2 cannot be 0
: due to the equivalence of the prob measures, so (0,100/11)
| p*****k
发帖数: 318 | 11 salientxu, thx for the correction.
however, pricing the call as 10 would result arbitrage...
as you already pointed out, i guess shorting the stock is
an arbitrage in the first place | M*****y
发帖数: 666 | 12 actually, if call is not priced at 10, then there is arbitrage!
S - K = 10 = c - p. so c must be >= 10
there is no arbitrage if 100% S tomorrow is 110 as in risk neutral measure.
remember, as it is called derivative, any profit opportunity of underlining
shall not influence the price of derivative.
【在 p*****k 的大作中提到】
: salientxu, thx for the correction.
: however, pricing the call as 10 would result arbitrage...
: as you already pointed out, i guess shorting the stock is
: an arbitrage in the first place
| p*****k
发帖数: 318 | 13 MsPiggy, im probably saying something stupid again:
if the call is priced at 10, the arbitrage i had in mind is
to short 1 stock, long 1 call and deposit the rest of 100
into the bank account.
seems the nonzero prob of the stock being 0 tmr results
the arbitrage, no? |
|
