8,674 research outputs found
On non-existence of a one factor interest rate model for volatility averaged generalized Fong-Vasicek term structures
The purpose of this paper is to study the generalized Fong--Vasicek
two-factor interest rate model with stochastic volatility. In this model the
dispersion of the stochastic short rate (square of volatility) is assumed to be
stochastic as well and it follows a non-negative process with volatility
proportional to the square root of dispersion. The drift of the stochastic
process for the dispersion is assumed to be in a rather general form including,
in particular, linear function having one root (yielding the original
Fong--Vasicek model or a cubic like function having three roots (yielding a
generalized Fong--Vasicek model for description of the volatility clustering).
We consider averaged bond prices with respect to the limiting distribution of
stochastic dispersion. The averaged bond prices depend on time and current
level of the short rate like it is the case in many popular one-factor interest
rate model including in particular the Vasicek and Cox--Ingersoll-Ross model.
However, as a main result of this paper we show that there is no such
one-factor model yielding the same bond prices as the averaged values described
above
Financial model calibration using consistency hints
We introduce a technique for forcing the calibration of a financial model to produce valid parameters. The technique is based on learning from hints. It converts simple curve fitting into genuine calibration, where broad conclusions can be inferred from parameter values. The technique augments the error function of curve fitting with consistency hint error functions based on the Kullback-Leibler distance. We introduce an efficient EM-type optimization algorithm tailored to this technique. We also introduce other consistency hints, and balance their weights using canonical errors. We calibrate the correlated multifactor Vasicek model of interest rates, and apply it successfully to Japanese Yen swaps market and US dollar yield market
Cross sectional efficient estimation of stochastic volatility short rate models
We consider the problem of estimation of term structure of interest rates. Filtering theory approach is very natural here with the underlying setup being non-linear and non-Gaussian. Earlier works make use of Extended Kalman Filter (EKF). However, the EKF in this situation leads to inconsistent estimation of parameters, though without high bias. One way to avoid this is to use methods like Efficient Method of Moments or Indirect Inference Method. These methods, however, are numerically very demanding. We use Kitagawa type scheme for nonlinear filtering problem, which solves the inconsistency problem without being numerically so demanding. \u
Praesphaerammina, a new genus of Cenozoic deep-water agglutinated foraminifera from the Carpathian flysch deposits
The genus Praesphaerammina Kaminski and Filipcscu is newly described based on a revision of the type species Cystammina subgaleata Vasicek 1947. The genus differs from the Holocene genus Sphaerammina Cushman 1910 emend. Loeblich and Tappan 1964, in possessing a less embracing final chamber and in its interio-areal to areal aperture that lacks any tooth. The definition of the subfamily Sphaeramminae is accordingly emended as well. The genus is common in the Eocene of the Carpathian flysch deposits, but the type species Praesphaerammina subgaleata (Vasicek 1947) is also observed in the Caribbean region and West Africa, where it ranges into the Miocene
MQLV: Optimal Policy of Money Management in Retail Banking with Q-Learning
Reinforcement learning has become one of the best approach to train a
computer game emulator capable of human level performance. In a reinforcement
learning approach, an optimal value function is learned across a set of
actions, or decisions, that leads to a set of states giving different rewards,
with the objective to maximize the overall reward. A policy assigns to each
state-action pairs an expected return. We call an optimal policy a policy for
which the value function is optimal. QLBS, Q-Learner in the
Black-Scholes(-Merton) Worlds, applies the reinforcement learning concepts, and
noticeably, the popular Q-learning algorithm, to the financial stochastic model
of Black, Scholes and Merton. It is, however, specifically optimized for the
geometric Brownian motion and the vanilla options. Its range of application is,
therefore, limited to vanilla option pricing within financial markets. We
propose MQLV, Modified Q-Learner for the Vasicek model, a new reinforcement
learning approach that determines the optimal policy of money management based
on the aggregated financial transactions of the clients. It unlocks new
frontiers to establish personalized credit card limits or to fulfill bank loan
applications, targeting the retail banking industry. MQLV extends the
simulation to mean reverting stochastic diffusion processes and it uses a
digital function, a Heaviside step function expressed in its discrete form, to
estimate the probability of a future event such as a payment default. In our
experiments, we first show the similarities between a set of historical
financial transactions and Vasicek generated transactions and, then, we
underline the potential of MQLV on generated Monte Carlo simulations. Finally,
MQLV is the first Q-learning Vasicek-based methodology addressing transparent
decision making processes in retail banking
The Heston model under stochastic interest rates
Tese de mestrado, Matemática Financeira, Faculdade de Ciências, Universidade de Lisboa,2008In this dissertation the Heston (1993) model is considered, but using, instead of a constant interest rate, stochastic interest rates according to Vasicek (1977) and to Cox, Ingersoll and Ross (1985) models. Under this framework, a closed-form solution is determined for the price of European standard calls, which, by using a manipulation implemented by Attari (2004), only require the evaluation of one characteristic function. For forward-start European calls, starting from the result for standard calls and using analytic characteristic functions, it is determined a closed-form solution that only requires one numerical integration. In the end, the results of these closedform solutions are compared with the results presented by Monte Carlo simulations for the considered models.Nesta dissertação é considerado o modelo de Heston (1993), mas em vez de utilizar uma taxa de juro constante, considera-se taxas de juro estocásticas segundo os modelos de Vasicek (1977) e de Cox, Ingersoll e Ross (1985). Neste contexto, é determinada uma solução fechada para a avaliação de standard calls Europeias, que, por ter sido usada uma manipulação implementada por Attari (2004), apenas necessitará da avaliação de uma função característica. Para calls forward-start Europeias, partindo do resultado apresentado para standard calls e utilizando funções característica analíticas, é determinada uma solução fechada que também recorrerá a apenas uma integração numérica. No final, os resultados destas fórmulas fechadas são comparados com os resultantes de simulações de Monte Carlo para os modelos considerados
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