Python for Finance: Analyze Big Financial Data

a mixed approach, using Euler for the index and the noncentral chi square-based exact approach for the volatili ...

Figure 10-12. Simulated stochastic volatility model paths Finally, let us take a brief look at the stati ...

Drift correction for jump to maintain risk neutrality σ Constant volatility of S Zt Standard Brownian motio ...

Since we have assumed a highly negative mean for the jump, it should not come as a surprise that the ...

In [ 45 ]: print “%15s %15s” % (‘Mean’, ‘Std. Deviation’) print 31 * “-” for i in range( 1 , 31 , 2 ): npr.se ...

-0.000000000000 0.999641436845 -0.000000000000 0.999642768905 -0.000000000000 0.999638303451 As you immediately noti ...

Valuation One of the most important applications of Monte Carlo simulation is the valuation of contingent c ...

In [ 56 ]: S0 = 100. r = 0.05 sigma = 0.25 T = 1.0 I = 50000 def gbm_mcs_stat(K): ”’ Valuation of Europ ...

Out[59]: 7.9500085250284336 In [ 60 ]: gbm_mcs_dyna(K=110., option=‘put’) Out[60]: 12.629934942682004 The question ...

Figure 10-15. Comparison of static and dynamic Monte Carlo estimator values A similar picture emerges for the dyna ...

The algorithm we describe in the following is called Least-Squares Monte Carlo (LSM) and is from the ...

dt = T / M df = np.exp(-r * dt) # simulation of index levels S = np.zeros((M + 1 , I)) S[ 0 ] = ...

Figure 10-17. Comparison of European and LSM Monte Carlo estimator values ...

Risk Measures In addition to valuation, risk management is another important application area of stochastic me ...

Figure 10-18. Absolute returns of geometric Brownian motion (30d) Having the ndarray object with the sorted r ...

Figure 10-19. Absolute returns of jump diffusion (30d) For this process and parameterization, the VaR over ...

Figure 10-20. Value-at-risk for geometric Brownian motion and jump diffusion Credit Value Adjustments Other i ...

In [ 85 ]: S0_CVA = np.exp(-r * T) * 1 / I * np.sum(( 1 - L * D) * ST) S0_CVA Out[85]: 99.466624 ...

Out[91]: 10.373513531207843 Compared to the case of a regular asset, the option case has somewhat different ...

Conclusions This chapter deals with methods and techniques important to the application of Monte Carlo simulation ...