Interest rate modeling for pricing and hedging
derivatives
We are currently working on the implementation
of a "forward Libor" market model (also known as BGM model), using analytical
approximations for swaptions implied volatilities (prices) so as to jointly
calibrate the cap and swaption markets. We have considered several formulations
for the forward rates instantaneous covariance structure and tested the
goodness of these approximations. We have developed routines for the pricing
of a large class of exotic products.
We are also implementing an extension of the
BGM model allowing for uncertainty in the forward rate volatilities
so as to consistently price smile effects.
In the past, we implemented some of the major
short rate models, namely the Black-Karasinski (1991) model, a version
of the Hull-White (1994) two factor model and our extension of the Cox-Ingersoll-Ross
(1985) model .
We also developed a proprietary functions library
for the pricing of exotic instruments such as Bermudan-style swaptions,
zero coupon swaptions, captions/floortions, CMS, options on CMS, quanto
derivatives such as quanto caps, quanto CMS, quanto swaptions
and differential swaps and others.
Pricing volatility smiles/skews
We have developed several versions
of an analytically tractable asset price model based on mixtures of lognormal
densities. The advantages of our model can be summarized as follows: i)
the asset price dynamics are explicitly given; ii) the model is analytically
tractable implying closed form formulas for European options and the relative
Greeks; iii) the marginal distribution of the asset price process is explicitly
known; iv) there is a controllable and potentially unlimited number of
parameters in the model; v) the market is complete. As a consequence, the
model calibration to market data and the computation of Greeks can be extremely
rapid and accurate. Moreover, exotic claims can be priced through a Monte
Carlo procedure.
The model is very general. In fact,
it can be applied to a number of different markets: equity, exchange rate
and interest rate markets.
Constant Proportion Portfolio
Insurance (CPPI)
We have analyzed the performance
of a CPPI strategy by simulating scenarios under several market situations
and by using historical data of some major stock indices.
We have proposed and implemented
alternative strategies with the ultimate aim of achieving a better average
performance. Simulations have been carried out under jump-diffusion models
and stochastic volatility models, both with stochastic and deterministic
interest rates.
We have explicitly calculated the
probability of default of the strategy under different assumptions. We
accordingly priced the risk of not achieving a given protection level at
maturity. We have also calculated the average time elapsing between consecutive
rebalancing events, which occur when the underlying asset returns exceed
a given threshold. |
MY MAIN TASKS AT BANCA IMI