Sage Journals: Discover world-class research

Abstract

This study endeavours to find an impeccable option-pricing model to meet the requirements of ‘Options’ practitioners during a tumultuous period. It encompasses ‘smile’ and ‘skew’ characters exhibiting price bias across moneyness and maturity. For the same, we compared and contrasted the classical Black–Scholes model with deterministic and stochastic volatility models. In order to make applicability of models more prominent, the hypothetical model has been put into practical implication of Nifty index options of India. Also, to ensure the model’s all-round applicability, they all have been passed through the most dramatic phase of the Indian financial economy spanning 2006–11, an ideal time to examine the sustainability of such models. Accuracy of model prices has been testified relative to the market, using the well-known error metrics. This research suggests that the deterministic volatility function (DVF) is the most suitable framework to price the Nifty index options. It not only out passes the benchmark Black–Scholes model but also dominates its stochastic counterpart the stochastic alpha, beta and rho (SABR) model.

JEL Classification: C01, C13, C52, C53, G17

Keywords

Black–Scholes call options deterministic volatility function implied volatility Nifty index options SABR stochastic

Get full access to this article

View all access options for this article.

References

Amin

and Victor

(1993), ‘Option Valuation with Systematic Stochastic Volatility’, Journal of Finance, 48(3): 881–910.

Bachelier

(1900), ‘Théorie de la spéculation’, Annales Scientifiques de l’École Normale Supérieure, 3(17): 21–86 (English translation in Cootner

(ed.) (1964), The Random Character of Stock Prices. MIT Press, reprinted London: Risk Books, 2000).

Backus

, Foresi

and Wu

(1997), ‘Accounting for Biases in Black-Scholes’, CRIF Working Paper series, Paper 30, New York University.

Bakshi

, Cao

and Chen

(1997), ‘Empirical Performance of Alternative Option Pricing Models’, Journal of Finance, 52(5): 2003–49.

Bates

D.S.

(1996), ‘Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutschemark Option’, Review of Financial Studies, 9(1): 69–107.

Black

(1976), ‘The Pricing of Commodity Contracts’, Journal of Financial Economics, 3(1–2): 167–79.

Black

and Scholes

(1973), ‘The Pricing of Options and Corporate Liabilities’, Journal of Political Economy, 81(3): 637–59.

Brockman

and Chowdhury

(1997), ‘Deterministic versus Stochastic Volatilities: Implications for Option Pricing Models’, Applied Financial Economics, 7(6): 499–505.

Canina

and Figlewski

(1993), ‘The Informational Content of Implied Volatility’, Review of Financial Studies, 6(3): 659–81.

10.

Christensen

B.J.

and Prabhala

N.R.

(1998), ‘The Relation between Implied and Realized Volatility’, Journal of Financial Economics, 50(2): 125–50.

11.

Christoffersen

and Jacobs

(2004), ‘The Importance of the Loss Function in Option Pricing’, Journal of Financial Econometrics, 72(2): 291–318.

12.

Cox

and Ross

(1976), ‘The Valuation of Options for Alternative Stochastic Processes’, Journal of Financial Economics, 3(1): 145–66.

13.

Cox

, Ross

and Rubinstein

(1979), ‘Option Pricing, a Simplified Approach’, Journal of Financial Economics, 7(3): 229–63.

14.

Day

T.E.

and Craig

M.L.

(1992), ‘Stock Market Volatility and the Information Content of Stock Index Options’, Journal of Econometrics, 52(1–2): 267–87.

15.

Derman

and Kani

(1994), ‘Riding on the Smile’, Risk, 7(2): 32–9.

16.

Dumas

, Fleming

and Whaley

(1998), ‘Implementing Volatility Functions: Empirical Tests’, Journal of Finance, 53(6): 2059–106.

17.

Dupire

(1994), ‘Pricing with a Smile’, Risk, 7(1): 18–20.

18.

Ederington

L.H.

and Guan

(2002), ‘Is Implied Volatility an Informationally Efficient and Effective Predictor of Future Volatility’, Journal of Risk, 4(3): 29–46.

19.

Edey

and Elliot

(1992), ‘Some Evidence on Option Prices as Predictors of Volatility’, Oxford Bulletin of Economics & Statistics, 54(4): 567–78.

20.

Feinstein

S.P.

(1989), ‘The BS Formula is Nearly Linear in Sigma for At-The-Money Options; Therefore Implied Volatilities from At-The-Money Options are Virtually Unbiased’, Working paper #88–9, Federal Reserve Bank, Atlanta.

21.

Glosten

L.R.

, Jagannathan

and Runkle

D.E.

(1993), ‘On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks’, Journal of Finance, 48(5): 1779–801.

22.

Hagan

P.S.

, Kumar

, Lesniewski

A.S.

and Woodward

D.E.

(2002), ‘Managing Smile Risk’, Wilmott Magazine, 22(August): 84–108.

23.

Heston

S.L.

(1993), ‘A Closed-form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options’, Review of Financial Studies, 6(2): 327–43.

24.

Heston

and Nandi

(2000), ‘A Closed-form GARCH Option Valuation Model’, Review of Financial Studies, 13(3): 585–625.

25.

Hull

and White

(1987), ‘The Pricing of Options on Assets with Stochastic Volatility’, Journal of Finance, 42(2): 281–300.

26.

Hull

and White

(1988), ‘An Analysis of the Bias in Option Pricing Caused by a Stochastic Volatility’, Advances in Futures and Options Research, 3(1988): 29–61.

27.

Johnson

and Shannon

(1987), ‘Option Pricing when the Variance is Changing’, Journal of Financial and Quantitative Analysis, 22(2): 143–51.

28.

Mayhew

(1995), ‘Implied Volatility’, Financial Analyst Journal, 51(4): 8–20.

29.

Poteshman

A.M.

(2000), ‘Forecasting Future Volatility from Option Prices’, Working Paper, University of Illinois at Urbana-Champaign.

30.

Scott

L.O.

(1987), ‘Option Pricing When The Variance Changes Randomly: Theory, Estimation and an Application’, Journal of Financial and Quantitative Analysis, 22(4): 419–38.

31.

Stein

E.M.

and Stein

J.C.

(1991), ‘Stock Price Distributions with Stochastic Volatility: An Analytic Approach’, Review of Financial Studies, 4(4): 727–52.

32.

Wiggins

J.B.

(1987), ‘Option Values under Stochastic Volatilities. Theory and Empirical Estimates’, Journal of Financial Economics, 19(2): 351–72.

Conjoint Analysis of Option and Volatility Models

Abstract

Keywords

Get full access to this article

References