An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model

Xin-Jiang He; Wenting Chen

Applications of Mathematics (2019)

  • Volume: 64, Issue: 3, page 367-382
  • ISSN: 0862-7940

Abstract

top
We consider the pricing of credit default swaps (CDSs) with the reference asset assumed to follow a geometric Brownian motion with a fast mean-reverting stochastic volatility, which is often observed in the financial market. To establish the pricing mechanics of the CDS, we set up a default model, under which the fair price of the CDS containing the unknown ``no default'' probability is derived first. It is shown that the ``no default'' probability is equivalent to the price of a down-and-out binary option written on the same reference asset. Based on the perturbation approach, we obtain an approximated but closed-form pricing formula for the spread of the CDS. It is also shown that the accuracy of our solution is in the order of $\mathscr O(\epsilon )$.

How to cite

top

He, Xin-Jiang, and Chen, Wenting. "An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model." Applications of Mathematics 64.3 (2019): 367-382. <http://eudml.org/doc/294529>.

@article{He2019,
abstract = {We consider the pricing of credit default swaps (CDSs) with the reference asset assumed to follow a geometric Brownian motion with a fast mean-reverting stochastic volatility, which is often observed in the financial market. To establish the pricing mechanics of the CDS, we set up a default model, under which the fair price of the CDS containing the unknown ``no default'' probability is derived first. It is shown that the ``no default'' probability is equivalent to the price of a down-and-out binary option written on the same reference asset. Based on the perturbation approach, we obtain an approximated but closed-form pricing formula for the spread of the CDS. It is also shown that the accuracy of our solution is in the order of $\mathscr O(\epsilon )$.},
author = {He, Xin-Jiang, Chen, Wenting},
journal = {Applications of Mathematics},
language = {eng},
number = {3},
pages = {367-382},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model},
url = {http://eudml.org/doc/294529},
volume = {64},
year = {2019},
}

TY - JOUR
AU - He, Xin-Jiang
AU - Chen, Wenting
TI - An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 3
SP - 367
EP - 382
AB - We consider the pricing of credit default swaps (CDSs) with the reference asset assumed to follow a geometric Brownian motion with a fast mean-reverting stochastic volatility, which is often observed in the financial market. To establish the pricing mechanics of the CDS, we set up a default model, under which the fair price of the CDS containing the unknown ``no default'' probability is derived first. It is shown that the ``no default'' probability is equivalent to the price of a down-and-out binary option written on the same reference asset. Based on the perturbation approach, we obtain an approximated but closed-form pricing formula for the spread of the CDS. It is also shown that the accuracy of our solution is in the order of $\mathscr O(\epsilon )$.
LA - eng
UR - http://eudml.org/doc/294529
ER -

References

top
  1. Beckers, S., 10.1086/296188, J. Business 56 (1983), 97-112. (1983) MR2695462DOI10.1086/296188
  2. Brigo, D., Chourdakis, K., 10.1142/S0219024909005567, Int. J. Theor. Appl. Finance 12 (2009), 1007-1026. (2009) Zbl1187.91206MR2574492DOI10.1142/S0219024909005567
  3. Cariboni, J., Schoutens, W., 10.21314/jcf.2007.172, J. Comput. Finance 10 (2007), 71-91. (2007) DOI10.21314/jcf.2007.172
  4. Malherbe, E. De, 10.21314/jor.2006.130, J. Risk 8 (2006), 85-113. (2006) DOI10.21314/jor.2006.130
  5. Duffie, D., Singleton, K. J., 10.1111/j.1540-6261.1997.tb01111.x, J. Finance 52 (1997), 1287-1321. (1997) DOI10.1111/j.1540-6261.1997.tb01111.x
  6. Fouque, J.-P., Papanicolaou, G., Sircar, K. R., Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, Cambridge, (2000). (2000) Zbl0954.91025MR1768877
  7. Fouque, J.-P., Papanicolaou, G., Sircar, K. R., 10.1142/S0219024900000061, Int. J. Theor. Appl. Finance 3 (2000), 101-142. (2000) Zbl1153.91497DOI10.1142/S0219024900000061
  8. Fouque, J.-P., Papanicolaou, G., Sircar, K. R., Solna, K., 10.1137/S0036139902401550, SIAM J. Appl. Math. 63 (2003), 1648-1665. (2003) Zbl1039.91024MR2001213DOI10.1137/S0036139902401550
  9. He, X., Chen, W., /10.1016/j.physa.2014.02.046, Physica A 404 (2014), 26-33. (2014) Zbl1402.91847MR3188756DOI/10.1016/j.physa.2014.02.046
  10. Jarrow, R. A., Turnbull, S. M., 10.1111/j.1540-6261.1995.tb05167.x, J. Finance 50 (1995), 53-86. (1995) DOI10.1111/j.1540-6261.1995.tb05167.x
  11. Joy, R. C., Schlig, E. S., 10.1109/t-ed.1970.17035, IEEE Transactions on Electron Devices 17 (1970), 586-594. (1970) DOI10.1109/t-ed.1970.17035
  12. Longstaff, F. A., Schwartz, E. S., 10.1111/j.1540-6261.1995.tb04037.x, J. Finance 50 (1995), 789-819. (1995) DOI10.1111/j.1540-6261.1995.tb04037.x
  13. Merton, R. C., 10.2307/2978814, J. Finance 29 (1974), 449-470. (1974) MR3235242DOI10.2307/2978814
  14. O'Kane, D., Turnbull, S., Valuation of credit default swaps, QCR Quarterly 2003-Q1/Q2 (2003), 17 pages. (2003) 
  15. Ramm, A. G., 10.2307/2695558, Am. Math. Mon. 108 (2001), 855-860. (2001) Zbl1036.47005MR1864050DOI10.2307/2695558
  16. Shreve, S. E., Stochastic Calculus for Finance II. Continuous-Time Models, Springer Finance, Springer, New York (2004). (2004) Zbl1068.91041MR2057928
  17. Tavella, D., Randall, C., Pricing Financial Instruments: The Tinite Difference Method, John Wiley & Sons, New York (2000). (2000) 
  18. Zhou, C., 10.1016/s0378-4266(00)00168-0, J. Banking & Finance 25 (2005), 2015-2040. (2005) DOI10.1016/s0378-4266(00)00168-0
  19. Zhu, S.-P., Chen, W.-T., 10.1016/j.aml.2011.04.011, Appl. Math. Lett. 24 (2011), 1663-1669. (2011) Zbl1216.91035MR2803003DOI10.1016/j.aml.2011.04.011

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.