Valuing Coupon Bond Linked to Variable Interest Rate

The paper analyses coupon bonds linked to variable interest rate in a contingent claim approach such that it can be decomposed in elementary options on interest rate and options to default. It is considered the case of continuous arithmetic average of interest rate in a simple capitalization to value the variable coupon paid by the bonds at maturity. The paper determines the expected interest rate on the bonds and the risk spread due to the default risk.Contingent claim, Asian option, Stochastic continuous process

Asset Liability Management for Banks

The model, by using a contingent claim approach, determines the fair value of the banks liabilities accounting for the protection and the surrender possibility. Furthermore, it determines the implied duration of banks liabilities so to show that the surrender possibility will reduce the effective duration of banks liabilities. Implications for the immunization are also treated

Asset Liability Management in Insurance Company

The model, by using the option theory, determines the fair value of the insurance life policies with different time of maturity and shows that the effective liabilities duration of an Insurance Company exposed to the default risk is different from the duration of a default free zero coupon bond with the same time of maturity. Furthermore, it shows that the value of equity can be immunized in a dynamic way with respect to the movement of the spot rate by selling and purchasing the default free bonds in the firm asset. Moreover, the equity value, by the right bond allocation, can be immunized without varying continually the weight of the bonds on the firm asset. Furthermore, it considers the surrender option and the mortally issue such that it corrects some pitfalls that are commonly encountered in the insurance industry

Asset Liability Management in Insurance Company

The model, by using the option theory, determines the fair value of the insurance life policies with different time of maturity and shows that the effective liabilities duration of an Insurance Company exposed to the default risk is different from the duration of a default free zero coupon bond with the same time of maturity. Furthermore, it shows that the value of equity can be immunized in a dynamic way with respect to the movement of the spot rate by selling and purchasing the default free bonds in the firm asset. Moreover, the equity value, by the right bond allocation, can be immunized without varying continually the weight of the bonds on the firm asset. Furthermore, it considers the surrender option and the mortally issue such that it corrects some pitfalls that are commonly encountered in the insurance industry

Credit Derivatives

The article presents a survey of the principal quantitative tools adopted by the major financial institutions in the credit market, pointing out their limits and new directions

Martingale Model

The model determines a stochastic continuous process as continuous limit of a stochastic discrete process so to show that the stochastic continuous process converges to the stochastic discrete process such that we can integrate it. Furthermore, the model determines the expected volatility and the expected mean so to show that the volatility and the mean are increasing function of the time

Financial Methods: A Quantitative Approach

The study analyses finite difference methods and stochastic volatility for option pricing model till Asian and Barrier options. Simulated result is presented with VBA code. The interest rate models is analyzed in arbitrage setting e simulated environment by using an affine term structure and the drift condition in combination with inflation model by measuring the liquidity and risk premium by presenting an efficient Monte Carlo simulator. Structural Model is presented in single time maturity and default barrier in first passage model. The intensity model is also faced by analyzing the liquidity e risk premium with copula approaches as wel

Finance & Stochastic

The study analyses quantitative models for financial markets by starting from geometric Brown process and Wiener process by analyzing Ito’s lemma and first passage model. Furthermore, it is analyzed the prices of the options, Vanilla & Exotic, by using the expected value and numerical model with geometric applications. From contingent claim approach ALM strategies are also analyzed so to get the effective duration measure of liabilities by assuming that clients buy options for protection and liquidity by assuming defaults protection barrier as well. Furthermore, the study analyses interest rate models by showing that the yields curve is given by the average of the expected short rates & variation of GDP with the liquidity risk, but in the case we have crisis it is possible to have risk premium as well, the study is based on simulated modelisation by using the drift condition in combination with the inflation models as expectation of the markets. Moreover, the CIR process is considered as well by getting with modification of the diffusion process the same result of the simulated modelisation but we have to consider that the CIR process is considered in the simulated environment as well. The credit risk model is considered as well in intensity model & structural model by getting the liquidity and risk premium and the PD probability from the Rating Matrix as well by using the diagonal. Furthermore, the systemic risk is considered as well by using a deco relation concept by copula approaches. Moreover, along the equilibrium condition between financial markets is achieved the equity pricing with implications for the portfolio construction in simulated environment with Bayesian applications for Smart Beta.. Finally, Value at Risk is also analyzed both static and dynamic with implications for the percentile of daily return and the tails risks by using a simulated approach