Reconstructing the CRR model knowing put and call prices
Reconstructing the CRR model knowing put and call prices
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Analysis · External communityPost link
External question — Quantitative Finance Stack Exchange
Author: Analysis
Original post: https://quant.stackexchange.com/questions/76463
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In an arbitrage-free single-period CRR model, the following options on a share are offered:
[They are all European]
(i) Call option at strike price
$100$
, price:
$C_{0,1}=7.44$
(ii) Call option at strike price
$110$
, price:
$C_{0,1}=3.72$
(iii) Put option at strike price
$100$
, price:
$P_{0,1}=23.59$
(iv) Put option at strike price
$110$
, price:
$P_{0,1}=29.49$
Show that given this information the model is fully specified.
Using the Put-Call parity I got
$7.44-23.59=S_0-100/(1+r)$
and
$3.72-29.49=S_0-110/(1+r)$
which yields
$S_0\approx 80$
and
$r\approx 0.04$
.
How can I get
$u,d$
?
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Ledog · External communityPost link
External answer — Quantitative Finance Stack Exchange
Author: Ledog
Original post: https://quant.stackexchange.com/a/76475
License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/
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I suppose by finding martingale measure. If then
$u = 1+b, d = 1+a$
, the probability of going to the up state is given by
$p = \frac{r-a}{b-a}$
.
$(r \in (a,b))$
. The second equation needed to solve for u and d is
$ud=1$
. Not 100% sure about this approach so please correct me if I'm wrong
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Quoted from Forex.com.bd-Editorial External question — Quantitative Finance Stack Exchange Author: Analysis Source score (net votes, not local likes): 0 Original post: https://quant.stackexchange.com/questions/76463 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. In an arbitrage-free single-period CRR model, the following options on a share are offered: [They are all European] (i) Call option at strike price $100$ , price: $C_{0,1}=7.44$ (ii) Call option at strike price $110$ , price: $C_{0,1}=3.72$ (iii) Put option at strike price $100$ , price: $P_{0,1}=23.59$ (iv) Put option at strike price $110$ , price: $P_{0,1}=29.49$ Show that given this information the model is fully specified. Using the Put-Call parity I got $7.44-23.59=S_0-100/(1+r)$ and $3.72-29.49=S_0-110/(1+r)$ which yields $S_0\approx 80$ and $r\approx 0.04$ . How can I get $u,d$ ?
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