Valuing Exchange Options under an Ornstein-Uhlenbeck Covariance Model
Round 1
Reviewer 1 Report
The paper is very dense but readable. It considers the pricing of spread options under a dynamic model with a complex correlation structure allowing random jumps, heavy-tails, asymmetric and stochastic behavior.
Authors should better justify the choice of the parameter sets. For example, their choice gives reasonable values of the average variances/covariances/correlations?
Figure 4: reduces the xaxis to 0-1.
Page 13, line 248: "Alternatively, the constrained moments can be directly calculated from the pdf of v + T 248 . In turn, the pdf of v + T 249 is computed via its characteristic function by inverse FFT. " May be I missed the point: if you have the pdf via numerical inversion of the FFT is not better to integrate the (conditional) Margrabe formula with respect to the density instead of using the series expansion?
The numerical results are limited. May be some additional numerical results for different maturities could be interesting.
Nowadays, the main reference paper for spread options is: A general closed-form spread option pricing formula, R Caldana, G Fusai, Journal of Banking & Finance 37 (12), 4893-4906. This paper shoud be cited. Also does the approach proposed in the paper could be applied to the present model?
Author Response
"Please see attachment"
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This paper studies the pricing of exchange option under a Ornstein-Uhlenbeck covariance model.
I think that the paper is very interesting but is not well written. (There are many typos)
Therefore, this paper must be rewritten before publication.
I have some comments for a better paper.
1. Authors must check paragraph indentation. It need to standardize.
2. Authors must check the numbering of equations. For example. there are two equation (3)(line 88 and line 95) on page 3.
3. Authors must modify the figures and replace the locations of figures.
4. Most of references are rather old. Authors should do a more recent literature review for exchange options.
Recommended papers are as follows.
Pasricha, Puneet, and Xin-Jiang He.
"Skew-Brownian motion and pricing European exchange options." International Review of Financial Analysis 82 (2022): 102120.
Garces, Len Patrick Dominic M., and Gerald HL Cheang.
"A numerical approach to pricing exchange options under stochastic volatility and jump-diffusion dynamics." Quantitative Finance 21, no. 12 (2021): 2025-2054.
Kim, Geonwoo.
"Valuation of exchange option with credit risk in a hybrid model." Mathematics 8, no. 11 (2020): 2091.
Pasricha, Puneet, and Anubha Goel. "A closed-form pricing formula for European exchange options with stochastic volatility.
" Probability in the Engineering and Informational Sciences 36, no. 3 (2022): 606-615.
Pasricha, Puneet, and Anubha Goel.
"Pricing vulnerable power exchange options in an intensity based framework." Journal of Computational and Applied Mathematics 355 (2019): 106-115.
Jeon, Junkee, and Geonwoo Kim.
"Power Exchange Option with a Hybrid Credit Risk under Jump-Diffusion Model." Mathematics 10, no. 1 (2022): 53.
Author Response
"Please see the attachment."
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
I would recommend acceptance of the paper after revising it for the journal format.
