Covariance and correlation swaps for financial markets with Markov-modulated volatilities. (English) Zbl 1290.91167
The paper solves the pricing problem for the covariance and correlation swaps of financial markets with Markov-modulated volatilities. The stochastic volatility is driven by a two-state Markov chain. Numerical examples are based on the VIX and VXN volatility indices.
Reviewer: George Stoica (Saint John)
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 91B70 | Stochastic models in economics |
| 60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |
Keywords:
Markov-modulated volatility; covariance swaps; correlation swaps; VIX index; VXN index; variance swaps; volatility swapsReferences:
| [1] | DOI: 10.1080/13504860601170609 · Zbl 1141.91015 · doi:10.1080/13504860601170609 |
| [2] | Bossu S., Arbitrage Pricing of Equity Correlation Waps (2005) |
| [3] | Bossu S., A New Approach for Modelling and Pricing Correlation Swaps (2007) |
| [4] | DOI: 10.3905/jod.2008.702503 · doi:10.3905/jod.2008.702503 |
| [5] | DOI: 10.1142/S0219024908005032 · Zbl 1180.91283 · doi:10.1142/S0219024908005032 |
| [6] | Brockhaus O., Risk pp 92– |
| [7] | DOI: 10.1007/s00780-005-0155-x · Zbl 1096.91022 · doi:10.1007/s00780-005-0155-x |
| [8] | Carr P., Realized Volatility and Variance: Options Via Swaps (2007) |
| [9] | DOI: 10.1146/annurev.financial.050808.114304 · doi:10.1146/annurev.financial.050808.114304 |
| [10] | DOI: 10.1111/j.1540-6261.2009.01467.x · doi:10.1111/j.1540-6261.2009.01467.x |
| [11] | Elliott R. J., Appl. Math. Finance 14 |
| [12] | DOI: 10.1080/07362990701420118 · Zbl 1155.91380 · doi:10.1080/07362990701420118 |
| [13] | Elliott R. J., Hidden Markov Model in Finance (2007) · Zbl 1116.91007 |
| [14] | DOI: 10.1080/1350486042000254024 · Zbl 1108.91316 · doi:10.1080/1350486042000254024 |
| [15] | Sepp A., J. Comput. Finance 11 pp 33– · doi:10.21314/JCF.2008.185 |
| [16] | DOI: 10.1016/j.jbankfin.2005.04.025 · doi:10.1016/j.jbankfin.2005.04.025 |
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