Trading with Path-Dependent Effect: A Continuous-Time Cointegration Perspective

2020 ◽  
Author(s):  
Tingjin Yan ◽  
Hoi Ying Wong
Keyword(s):  
Continuous Time ◽  
Dependent Effect ◽  
Path Dependent

A CONTINUOUS-TIME REEXAMINATION OF DOLLAR-COST AVERAGING

2003 ◽  
Vol 06 (02) ◽  
pp. 173-194 ◽  
Author(s):  
MOSHE A. MILEVSKY ◽  
STEVEN E. POSNER
Keyword(s):  
Continuous Time ◽  
Asset Price ◽  
Theory And Practice ◽  
Financial Mathematics ◽  
Expected Return ◽  
Final Value ◽  
Lump Sum ◽  
Brownian Bridges ◽  
Payoff Structure ◽  
Path Dependent

The widespread practice of dollar-cost averaging (DCA) amongst the investing public, has puzzled most financial economists, ever since Constantinides [2] demonstrated the dynamic inefficiency of this strategy under very general conditions. This enduring phenomena has forced researchers, such as Statman [12], to suggest behavioral explanations for DCA's popularity, predicated on the prospect theory of Kahneman and Tversky [4]. In this paper we reexamine the payoff structure of DCA via continuous-time financial mathematics and then ask the question: Is it possible to reconcile the theory and practice of dollar-cost averaging? To answer this question, we take a slightly different approach to the issue by using the tools of stochastic calculus and Brownian bridges. We demonstrate that engaging in a dollar-cost averaging strategy is akin to purchasing a zero strike arithmetic Asian option on the underlying security. In other words, people who engage in dollar-cost averaging are implicitly purchasing a path-dependent contingent claim. We then prove that the expected return from this exotic option — i.e. the DCA strategy — conditional on knowing the final value of the security will uniformly exceed the return from the underlying security for all sufficiently large volatilities. This leads us to argue that investors may be dollar-cost averaging because they have "target prices" for the underlying asset price. The strategy of dollar-cost averaging would then exceed the returns from lump-sum investing, based on their subjective conditional expectation. In fact, the more volatile the underlying security, the greater is the benefit to dollar-cost averaging — conditional on knowing the final value — which is consistent with common practice.

A DYNAMIC APPROACH TO THE MODELING OF CORRELATION CREDIT DERIVATIVES USING MARKOV CHAINS

2009 ◽  
Vol 12 (01) ◽  
pp. 45-62 ◽  
Author(s):  
GIUSEPPE DI GRAZIANO ◽  
L. C. G. ROGERS
Keyword(s):  
Markov Process ◽  
Continuous Time ◽  
Credit Derivatives ◽  
Default Correlation ◽  
Dynamic Approach ◽  
New Approach ◽  
Industry Practice ◽  
Path Dependent ◽  
The Times ◽  
High Degree

The modeling of credit events is in effect the modeling of the times to default of various names. The distribution of individual times to default can be calibrated from CDS quotes, but for more complicated instruments, such as CDOs, the joint law is needed. Industry practice is to model this correlation using a copula/base correlation approach, which suffers significant deficiencies. We present a new approach to default correlation modeling, where defaults of different names are driven by a common continuous-time Markov process. Individual default probabilities and default correlations can be calculated in closed form. We provide semi-analytic formulas for the pricing of CDO tranches via Laplace-transform techniques which are both fast and easy to implement. The model calibrates to quoted tranche prices with a high degree of precision and allows one to price non-standard tranches in a consistent and arbitrage-free manner. The number of parameters of the model is flexible and can be adjusted to adapt to the set of market data one is calibrating to. More importantly, the model is dynamically consistent and can be used to price options on tranches and other exotic path-dependent products.

Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Asymptotic Formula ◽  
Continuous Time ◽  
Heavy Tails ◽  
Tail Behavior ◽  
Renewal Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

Moral reasoning is the process of asking moral questions and answering them

2019 ◽  
Vol 42 ◽  
Author(s):  
Mark Alfano
Keyword(s):  
Moral Reasoning ◽  
Dependent Process ◽  
Asking Questions ◽  
Path Dependent ◽  
Path Dependent Process ◽  
Moral Questions

Abstract Reasoning is the iterative, path-dependent process of asking questions and answering them. Moral reasoning is a species of such reasoning, so it is a matter of asking and answering moral questions, which requires both creativity and curiosity. As such, interventions and practices that help people ask more and better moral questions promise to improve moral reasoning.

Hierarchical Bayesian continuous time dynamic modeling.

2018 ◽  
Vol 23 (4) ◽  
pp. 774-799 ◽  
Author(s):  
Charles C. Driver ◽  
Manuel C. Voelkle
Keyword(s):  
Dynamic Modeling ◽  
Continuous Time ◽  
Hierarchical Bayesian ◽  
Time Dynamic

Continuous Time Controller Design

IEE Review ◽  
1991 ◽  
Vol 37 (6) ◽  
pp. 228
Author(s):  
Stephen Barnett
Keyword(s):  
Continuous Time ◽  
Controller Design
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