PRICING AND FILTERING IN A TWO-DIMENSIONAL DIVIDEND SWITCHING MODEL

2010 ◽  
Vol 13 (07) ◽  
pp. 1001-1017 ◽  
Author(s):  
PAVEL V. GAPEEV ◽  
MONIQUE JEANBLANC
Keyword(s):  
Asset Price ◽  
Contingent Claims ◽  
Conditional Probability Density ◽  
Random Drift ◽  
Brownian Motions ◽  
Risky Assets ◽  
Switching Model ◽  
The Times ◽  
Geometric Brownian Motions ◽  
Random Times

We study a model of a financial market in which the dividend rates of two risky assets change their initial values to other constant ones at the times at which certain unobservable external events occur. The asset price dynamics are described by geometric Brownian motions with random drift rates switching at exponential random times, that are independent of each other and the constantly correlated driving Brownian motions. We obtain closed form expressions for the rational values of European contingent claims through the filtering estimates of occurrence of the switching times and their conditional probability density derived given the filtration generated by the underlying asset price processes.

scholarly journals PRICING OF CONTINGENT CLAIMS IN A TWO-DIMENSIONAL MODEL WITH RANDOM DIVIDENDS

2009 ◽  
Vol 12 (08) ◽  
pp. 1091-1104 ◽  
Author(s):  
PAVEL V. GAPEEV ◽  
MONIQUE JEANBLANC
Keyword(s):  
Financial Market ◽  
Diffusion Processes ◽  
Partial Information ◽  
Asset Price ◽  
Contingent Claims ◽  
Dimensional Model ◽  
Random Drift ◽  
Brownian Motions ◽  
Risky Assets ◽  
Geometric Brownian Motions

We study a model of a financial market in which two risky assets are paying dividends with rates changing their initial values to other constant ones when certain events occur. Such events are associated with the first times at which the value processes of issuing firms, modeled by geometric Brownian motions, fall to some prescribed levels. The asset price dynamics are described by exponential diffusion processes with random drift rates and independent driving Brownian motions. We derive closed form expressions for rational values of European contingent claims, under full and partial information.

The design of pension contracts: on the perspective of customers

2018 ◽  
Vol 13 (2) ◽  
pp. 219-240 ◽  
Author(s):  
Zhaoxun Mei
Keyword(s):  
Young People ◽  
Utility Theory ◽  
Asset Price ◽  
Expected Utility Theory ◽  
Cumulative Prospect Theory ◽  
The Other ◽  
Risky Assets ◽  
Distribution Rule ◽  
Similar Product ◽  
Guarantee Rate

AbstractThis paper introduces a new pension contract which provides a smoothed return for the customer. The new contract protects customers from adverse asset price movements while keeping the potential of positive returns. It has a transparent structure and clear distribution rule, which can be easily understood by the customer. We compare the new contract to two other contracts under Cumulative Prospect Theory (CPT); one has a similar product structure but without guarantees and the other provides the same guarantee rate but with a different structure. The results show that the new contract is the most attractive contract for a CPT-maximising customer. Yet, we find different results if we let the customer be an Expected Utility Theory-maximising one. Moreover, this paper presents the static optimal portfolio for an individual customer. The results conform to the traditional pension advice that young people should invest more of their money in risky assets while older people should put more money in less risky assets.

scholarly journals CREDIT RISK PREMIA AND QUADRATIC BSDEs WITH A SINGLE JUMP

2010 ◽  
Vol 13 (07) ◽  
pp. 1103-1129 ◽  
Author(s):  
STEFAN ANKIRCHNER ◽  
CHRISTOPHETTE BLANCHET-SCALLIET ◽  
ANNE EYRAUD-LOISEL
Keyword(s):  
Credit Risk ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Risk Premia ◽  
Contingent Claims ◽  
Quadratic Growth ◽  
Utility Preferences ◽  
Random Times ◽  
Uniqueness Theory

This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indifference valuation principles. Assuming exponential utility preferences we derive representations of indifference premia of credit risk in terms of solutions of Backward Stochastic Differential Equations (BSDE). The class of BSDEs needed for that representation allows for quadratic growth generators and jumps at random times. Since the existence and uniqueness theory for this class of BSDEs has not yet been developed to the required generality, the first part of the paper is devoted to fill that gap. By using a simple constructive algorithm, and known results on continuous quadratic BSDEs, we provide sufficient conditions for the existence and uniqueness of quadratic BSDEs with discontinuities at random times.

ATTAINABLE CONTINGENT CLAIMS IN A MARKOVIAN REGIME-SWITCHING MARKET

2012 ◽  
Vol 15 (08) ◽  
pp. 1250055 ◽  
Author(s):  
ROBERT J. ELLIOTT ◽  
TAK KUEN SIU
Keyword(s):  
Regime Switching ◽  
Contingent Claims ◽  
Share Price ◽  
Regime Switching Model ◽  
Martingale Representation ◽  
Switching Model ◽  
Representation Result ◽  
Markovian Regime Switching ◽  
Coupon Bond ◽  
Markovian Regime

It is known that the market in a Markovian regime-switching model is, in general, incomplete, so not all contingent claims can be perfectly hedged. We show, in this paper, how certain contingent claims are attainable in the regime-switching market using a money market account, a share and a zero-coupon bond. General contingent claims with payoffs depending on both the share price and the state of the regime-switching process are considered. We apply a martingale representation result to show the attainability of a European-style contingent claim. We also extend our analysis to Asian-style and American-style contingent claims.

CMBS Tranche Valuation Framework: Correlated Geometric Brownian Motions Simulation

2011 ◽  
Vol 21 (1) ◽  
pp. 55-66 ◽  
Author(s):  
Peijie Shiu ◽  
Uyen Luong ◽  
Yadin Rozov
Keyword(s):  
Brownian Motions ◽  
Geometric Brownian Motions

The coupling of regenerative processes

1983 ◽  
Vol 15 (3) ◽  
pp. 531-561 ◽  
Author(s):  
Hermann Thorisson
Keyword(s):  
Initial Conditions ◽  
Random Variable ◽  
Total Variation Norm ◽  
Absolutely Continuous ◽  
Moment Conditions ◽  
Common Component ◽  
General State Space ◽  
Regeneration Times ◽  
The Times ◽  
Random Times

A distributional coupling concept is defined for continuous-time stochastic processes on a general state space and applied to processes having a certain non-time-homogeneous regeneration property: regeneration occurs at random times So, S1, · ·· forming an increasing Markov chain, the post-Sn process is conditionally independent of So, · ··, Sn–1 given Sn, and the conditional distribution is independent of n. The coupling problem is reduced to an investigation of the regeneration times So, S1, · ··, and a successful coupling is constructed under the condition that the recurrence times Xn+1 = Sn+1 – Sn given that , are stochastically dominated by an integrable random variable, and that the distributions , have a common component which is absolutely continuous with respect to Lebesgue measure (or aperiodic when the Sn's are lattice-valued). This yields results on the tendency to forget initial conditions as time tends to ∞. In particular, tendency towards equilibrium is obtained, provided the post-Sn process is independent of Sn. The ergodic results cover convergence and uniform convergence of distributions and mean measures in total variation norm. Rate results are also obtained under moment conditions on the Ps's and the times of the first regeneration.

scholarly journals Leaning against the Bubble: Central Bank Intervention in Walrasian Asset Markets

Risks ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 214
Author(s):  
Chia-Lin Chang ◽  
Jukka Ilomäki ◽  
Hannu Laurila
Keyword(s):  
Central Bank ◽  
Asset Price ◽  
Market Price ◽  
Market Model ◽  
Asset Markets ◽  
Central Bank Intervention ◽  
Risky Assets ◽  
Automatic Stabilizer ◽  
Negative Effect ◽  
Prediction Coefficient

The paper presents a two-period Walrasian financial market model composed of informed and uninformed rational investors, and noise traders. The rational investors maximize second period consumption utility from the payoffs of trading risk-free holdings to risky assets in the first period. The central bank reacts directly to asset price movements by selling or buying assets to stabilize the market price. It is found that the intervention makes the risky asset’s market price per share less sensitive to information shocks, which presses the market price towards its average price thus reducing price variance. The informed investors’ prediction coefficient remains unaffected, but that of the uninformed investors is magnified, which cancels out the negative effect on shock sensitivity thus keeping the expected value of the risky asset’s dividend constant. Finally, the introduction of the policy rule does not affect rational investors’ risk per share. A general conclusion is that the central bank’s policy can be regarded as an effective automatic stabilizer of financial markets.

scholarly journals A Technical Note, Looback Options: a comparison between Monte Carlo Techniques

2020 ◽  
Vol 14 (2) ◽  
pp. 119
Author(s):  
Marcelo González A. ◽  
Antonio Parisi F. ◽  
Arturo Rodríguez P.
Keyword(s):  
Monte Carlo ◽  
Performance Measures ◽  
Asset Price ◽  
Contingent Claims ◽  
Technical Note ◽  
Time Interval ◽  
Underlying Asset ◽  
Monte Carlo Techniques ◽  
Lookback Options ◽  
Path Dependent

Looback options are path dependent contingent claims whose payoffs depend on the extrema of the underlying asset price over a certain time interval. In this note we compare the performance of two Monte Carlo techniques to price lookback options, a crude Monte Carlo estimator and Antithetic variate estimator. We find that the Antithetic estimator performs better under a variety of performance measures.

scholarly journals Apreçamento de Ativos Referenciados em Volatilidade

2006 ◽  
Vol 4 (2) ◽  
pp. 203
Author(s):  
Alan De Genaro Dario
Keyword(s):  
Stochastic Volatility ◽  
Foreign Currency ◽  
Asset Price ◽  
Realized Volatility ◽  
Contingent Claims ◽  
Stochastic Volatility Model ◽  
Currency Options ◽  
Variance Swaps ◽  
Volatility Model ◽  
Future Realized Volatility

Volatility swaps are contingent claims on future realized volatility. Variance swaps are similar instruments on future realized variance, the square of future realized volatility. Unlike a plain vanilla option, whose volatility exposure is contaminated by its asset price dependence, volatility and variance swaps provide a pure exposure to volatility alone. This article discusses the risk-neutral valuation of volatility and variance swaps based on the framework outlined in the Heston (1993) stochastic volatility model. Additionally, the Heston (1993) model is calibrated for foreign currency options traded at BMF and its parameters are used to price swaps on volatility and variance of the BRL / USD exchange rate.

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