Abstract
We apply the local risk-minimization approach to defaultable claims and we compare it with intensity-based evaluation formulas and the mean-variance hedging. We solve analytically the problem of finding respectively the hedging strategy and the associated portfolio for the three methods in the case of a default put option with random recovery at maturity.
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Biagini, F., Cretarola, A.: Local risk-minimization for defaultable markets. Preprint, LMU University of München and University of Bologna (2006)
Biagini, F., Cretarola, A.: Local risk-minimization for defaultable claims with recovery process. Preprint, LMU University of München and University of Bologna (2006)
Biagini, F., Guasoni, P.: Mean-variance hedging with random volatility jumps. Stoch. Anal. Appl. 20, 471–494 (2002)
Biagini, F., Pratelli, M.: Local risk minimization and numéraire. J. Appl. Probab. 36(4), 1–14 (1999)
Biagini, F., Guasoni, P., Pratelli, M.: Mean-variance hedging for stochastic volatility models. Math. Financ. 10(2), 109–123 (2000)
Bielecki, T.R., Jeanblanc, M.: Indifference pricing of defaultable claims. In: Indifference Pricing, Theory and Applications, Financial Engineering. Princeton University Press, Princeton (2004)
Bielecki, T.R., Rutkowski, M.: Credit Risk: Modelling, Valuation and Hedging, 2nd edn. Springer, Berlin (2004)
Bielecki, T.R., Jeanblanc, M., Rutkowski, M.: Pricing and hedging of credit risk: replication and mean- variance approaches I. In: Mathematics of Finance. Contemp. Math., vol. 351, pp. 37–53. Amer. Math. Soc., Providence (2004)
Bielecki, T.R., Jeanblanc, M., Rutkowski, M.: Pricing and hedging of credit risk: replication and mean- variance approaches II. In: Mathematics of Finance. Contemp. Math., vol. 351, pp. 55–64. Amer. Math. Soc., Providence (2004)
Bielecki, T.R., Jeanblanc, M., Rutkowski, M.: Hedging of defaultable claims. In: Paris-Princeton Lectures on Mathematical Finance 2003. Lecture Notes in Mathematics, vol. 1847. Springer, Berlin (2004)
Bielecki, T.R., Jeanblanc, M., Rutkowski, M.: Modelling and valuation of credit risk. In: Stochastic Methods in Finance. Lecture Notes in Math., vol. 1856, pp. 27–126. Springer, Berlin (2004)
Covitz, D., Han, S.: An empirical analysis of bond recovery rates: exploring a structural view of default. Preprint, The Federal Reserve Board, Washington (2004)
Delbaen, F., Schachermayer, W.: The variance-optimal martingale measure for continuous processes. Bernoulli 2, 81–105 (1996); Amendments and corrections. Bernoulli 2, 379–380 (1996)
Dellacherie, C., Meyer, P.A.: Probabilities and Potential B: Theory of Martingales. North-Holland, Amsterdam (1982)
Föllmer, H., Schweizer, M.: Hedging of contingent claims under incomplete information. In: Eliot, R.J., Davis, M.H.A. (eds.) Applied Stochastic Analysis, pp. 389–414. Gordon & Breach, New York (1991)
Geman, H., El Karoui, N., Rochet, J.C.: Changes of numéraire, changes of probability measure and option pricing. J. App. Probab. 32, 443–458 (1995)
Heath, D., Platen, E., Schweizer, M.: A comparison of two quadratic approaches to hedging in incomplete markets. Math. Financ. 11, 385–413 (2001)
Møller, T.: Risk-minimizing hedging strategies for insurance payment processes. Financ. Stoch. 5, 419–446 (2001)
Protter, P.: Stochastic Integration and Differential Equations, Applications of Mathematics. Springer, Berlin (1990)
Øksendal, B.: Stochastic Differential Equations. Springer, Berlin (1998)
Rheinländer, T., Schweizer, M.: On L 2-projections on a space of stochastic integrals. Ann. Probab. 25, 1810–1831 (1997)
Schweizer, M.: On the minimal martingale measure and the Föllmer–Schweizer decomposition. Stoch. Anal. Appl. 13, 573–599 (1995)
Schweizer, M.: A guided tour through quadratic hedging approaches. In: Jouini, E., Cvitanic, J., Musiela, M. (eds.) Option Pricing, Interest Rates and Risk Management, pp. 538–574. Cambridge University Press, Cambridge (2001)
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Biagini, F., Cretarola, A. Quadratic Hedging Methods for Defaultable Claims. Appl Math Optim 56, 425–443 (2007). https://doi.org/10.1007/s00245-007-9005-x
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DOI: https://doi.org/10.1007/s00245-007-9005-x