Abstract
In finance, many option pricing models generalizing the Black-Scholes model do not have closed form, analytic solutions so that it is hard to compute the solutions or at least it requires much time to compute the solutions. Therefore, asymptotic representation of options prices of various type has important practical implications in finance. This paper presents asymptotic expansions of option prices in the constant elasticity of variance model as the parameter appearing in the exponent of the diffusion coefficient tends to 2 which corresponds to the well-known Black-Scholes model. We use perturbation theory for partial differential equations to obtain the relevant results for European vanilla, barrier, and lookback options. We make our application of perturbation theory mathematically rigorous by supplying error bounds.
| Original language | English |
|---|---|
| Pages (from-to) | 490-501 |
| Number of pages | 12 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 375 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2011 Mar 15 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Cite this
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Asymptotic option pricing under the CEV diffusion. / Park, Sang Hyeon; Kim, Jeong Hoon.
In: Journal of Mathematical Analysis and Applications, Vol. 375, No. 2, 15.03.2011, p. 490-501.Research output: Contribution to journal › Article
TY - JOUR
T1 - Asymptotic option pricing under the CEV diffusion
AU - Park, Sang Hyeon
AU - Kim, Jeong Hoon
PY - 2011/3/15
Y1 - 2011/3/15
N2 - In finance, many option pricing models generalizing the Black-Scholes model do not have closed form, analytic solutions so that it is hard to compute the solutions or at least it requires much time to compute the solutions. Therefore, asymptotic representation of options prices of various type has important practical implications in finance. This paper presents asymptotic expansions of option prices in the constant elasticity of variance model as the parameter appearing in the exponent of the diffusion coefficient tends to 2 which corresponds to the well-known Black-Scholes model. We use perturbation theory for partial differential equations to obtain the relevant results for European vanilla, barrier, and lookback options. We make our application of perturbation theory mathematically rigorous by supplying error bounds.
AB - In finance, many option pricing models generalizing the Black-Scholes model do not have closed form, analytic solutions so that it is hard to compute the solutions or at least it requires much time to compute the solutions. Therefore, asymptotic representation of options prices of various type has important practical implications in finance. This paper presents asymptotic expansions of option prices in the constant elasticity of variance model as the parameter appearing in the exponent of the diffusion coefficient tends to 2 which corresponds to the well-known Black-Scholes model. We use perturbation theory for partial differential equations to obtain the relevant results for European vanilla, barrier, and lookback options. We make our application of perturbation theory mathematically rigorous by supplying error bounds.
UR - http://www.scopus.com/inward/record.url?scp=78149410098&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78149410098&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2010.09.060
DO - 10.1016/j.jmaa.2010.09.060
M3 - Article
AN - SCOPUS:78149410098
VL - 375
SP - 490
EP - 501
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
ER -