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Accurate vega calculation for Bermudan swaptions. (English) Zbl 1420.91448
Ehrhardt, Matthias (ed.) et al., Novel methods in computational finance. Cham: Springer. Math. Ind. 25, 65-82 (2017).
Summary: Short rate models are widely used for pricing of Bermudan swaptions. In addition to prices, traders and risk managers need sensitivities for hedging and risk management. Vega is the sensitivity of the price with respect to changes in market volatilities (i.e. implied Black’76 or Bachelier volatilities). This sensitivity is of particular importance for Bermudan swaptions.
It is common practice to evaluate vega by shifting market data and re-evaluating model prices. Even though this procedure is often used, in practice it is inefficient here since the model calibration process flattens out the shift of single volatility surface grid points. Thus this procedure may underestimate sensitivities. In this chapter, we demonstrate how adjoint algorithmic differentiation can be used to calculate accurate and stable vegas without loss of performance.
For the entire collection see [Zbl 1390.91011].
MSC:
91G20 Derivative securities (option pricing, hedging, etc.)
Software:
dcc; dco/c++
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References:
[1] Brigo, D., Mercurio, F.: Interest Rate Models - Theory and Practice. Springer, Berlin (2007) · Zbl 1038.91040
[2] Capriotti, L.: Fast greeks by algorithmic differentiation. J. Comput. Finance 14, 3-35 (2011)
[3] Giles, M.B., Glasserman, P.: Smoking adjoints: fast Monte Carlo greeks. Risk 19, 88-92 (2006)s
[4] Griewank, A., Walther, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, 2nd edn. SIAM, Philadelphia (2008) · Zbl 1159.65026
[5] Henrard, M.: Adjoint algorithmic differentiation: calibration and implicit function theorem. Risk 17, 37-47 (2014)
[6] Hull, J.C., White, A.: Pricing interest-rate-derivative securities. Rev. Finance Stud. 3, 573-592 (1990) · Zbl 1386.91152
[7] Jamshidian, F.: An exact bond option pricing formula. J. Finance 44, 205-209 (1989)
[8] Leclerc, M., Liang, Q., Schneider, I.: Fast Monte Carlo Bermudan greeks. Risk 22, 84-88 (2009)
[9] Naumann, U.: The Art of Differentiating Computer Programs: An Introduction to Algorithmic Differentiation. SIAM, Philadelphia (2012) · Zbl 1275.65015
[10] Naumann, U., Leppkes, K., Lotz, J.: dco/C++ user guide. Technical Report, RWTH Aachen (2014). Technical Report AIB-2014-03
[11] Schlenkrich, S.: Evaluating sensitivities of Bermudan swaptions. Master’s thesis, University of Oxford (2011)
[12] Schlenkrich, S.: Efficient calibration of the Hull White model. Optim. Control Appl. Methods 33, 249-374 (2012) · Zbl 1277.93013
[13] Schlenkrich, S., Miemiec, A.: Choosing the right spread. Wilmott Mag. 60-67 (2015)
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