scholarly journals An exact and explicit formula for pricing lookback options with regime switching

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Leunglung Chan ◽  
Song-Ping Zhu
Keyword(s):  
Regime Switching ◽  
Closed Form Solution ◽  
Form Solution ◽  
Risky Asset ◽  
Chain Process ◽  
Switching Model ◽  
Lookback Options ◽  
State Regime ◽  
Markov Modulated ◽  
Appreciation Rate

<p style='text-indent:20px;'>This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geometric Brownian motion; that is, the appreciation rate and the volatility of the underlying risky asset depend on states of the economy described by a continuous-time Markov chain process. We derive an exact, explicit and closed-form solution for European-style lookback options in a two-state regime switching model.</p>

scholarly journals An Analytic Approach for Pricing American Options with Regime Switching

2021 ◽  
Vol 14 (5) ◽  
pp. 188
Author(s):  
Leunglung Chan ◽  
Song-Ping Zhu
Keyword(s):  
Regime Switching ◽  
American Options ◽  
Option Price ◽  
Switching Model ◽  
Homotopy Analysis ◽  
State Regime ◽  
Markov Modulated ◽  
Appreciation Rate ◽  
The Interest Rate ◽  
Hidden States

This paper investigates the American option price in a two-state regime-switching model. The dynamics of underlying are driven by a Markov-modulated Geometric Wiener process. That means the interest rate, the appreciation rate, and the volatility of underlying rely on hidden states of the economy which can be interpreted in terms of Markov chains. By means of the homotopy analysis method, an explicit formula for pricing two-state regime-switching American options is presented.

HEDGING OPTIONS IN A DOUBLY MARKOV-MODULATED FINANCIAL MARKET VIA STOCHASTIC FLOWS

2019 ◽  
Vol 22 (08) ◽  
pp. 1950047 ◽  
Author(s):  
TAK KUEN SIU ◽  
ROBERT J. ELLIOTT
Keyword(s):  
Markov Chain ◽  
Financial Market ◽  
Continuous Time ◽  
Regime Switching ◽  
Stochastic Flows ◽  
Finite State ◽  
Markov Modulated ◽  
Appreciation Rate ◽  
The Interest Rate ◽  
Over Time

The hedging of a European-style contingent claim is studied in a continuous-time doubly Markov-modulated financial market, where the interest rate of a bond is modulated by an observable, continuous-time, finite-state, Markov chain and the appreciation rate of a risky share is modulated by a continuous-time, finite-state, hidden Markov chain. The first chain describes the evolution of credit ratings of the bond over time while the second chain models the evolution of the hidden state of an underlying economy over time. Stochastic flows of diffeomorphisms are used to derive some hedge quantities, or Greeks, for the claim. A mixed filter-based and regime-switching Black–Scholes partial differential equation is obtained governing the price of the claim. It will be shown that the delta hedge ratio process obtained from stochastic flows is a risk-minimizing, admissible mean-self-financing portfolio process. Both the first-order and second-order Greeks will be considered.

Matrix product-form solutions for Markov chains with a tree structure

1994 ◽  
Vol 26 (04) ◽  
pp. 965-987 ◽  
Author(s):  
Raymond W. Yeung ◽  
Bhaskar Sengupta
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Closed Form Solution ◽  
Steady State Solution ◽  
Form Solution ◽  
Product Form ◽  
Matrix Product ◽  
Preemptive Resume ◽  
Finite Set ◽  
Markov Modulated

We have two aims in this paper. First, we generalize the well-known theory of matrix-geometric methods of Neuts to more complicated Markov chains. Second, we use the theory to solve a last-come-first-served queue with a generalized preemptive resume (LCFS-GPR) discipline. The structure of the Markov chain considered in this paper is one in which one of the variables can take values in a countable set, which is arranged in the form of a tree. The other variable takes values from a finite set. Each node of the tree can branch out into d other nodes. The steady-state solution of this Markov chain has a matrix product-form, which can be expressed as a function of d matrices Rl,· ··, Rd. We then use this theory to solve a multiclass LCFS-GPR queue, in which the service times have PH-distributions and arrivals are according to the Markov modulated Poisson process. In this discipline, when a customer's service is preempted in phase j (due to a new arrival), the resumption of service at a later time could take place in a phase which depends on j. We also obtain a closed form solution for the stationary distribution of an LCFS-GPR queue when the arrivals are Poisson. This result generalizes the known result on a LCFS preemptive resume queue, which can be obtained from Kelly's symmetric queue.

scholarly journals FOURIER TRANSFORM METHODS FOR REGIME-SWITCHING JUMP-DIFFUSIONS AND THE PRICING OF FORWARD STARTING OPTIONS

2012 ◽  
Vol 15 (05) ◽  
pp. 1250037 ◽  
Author(s):  
ALESSANDRO RAMPONI
Keyword(s):  
Fourier Transform ◽  
Regime Switching ◽  
Closed Form Solution ◽  
Jump Diffusion ◽  
Form Solution ◽  
Transform Method ◽  
Finite State ◽  
Jump Diffusion Model ◽  
Log Price ◽  
The Fourier Transform

In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strike to efficiently calculate the value of various types of options and as a concrete example of application, we present some numerical results within a two-state regime switching version of the Merton jump-diffusion model. Then we develop a closed-form solution to the problem of pricing a Forward Starting Option and use this result to approximate the value of such a derivative in a general stochastic volatility framework.

scholarly journals A GENERAL EQUILIBRIUM MODEL OF THE TERM STRUCTURE OF INTEREST RATES UNDER REGIME-SWITCHING RISK

2005 ◽  
Vol 08 (07) ◽  
pp. 839-869 ◽  
Author(s):  
SHU WU ◽  
YONG ZENG
Keyword(s):  
General Equilibrium ◽  
Interest Rates ◽  
Term Structure ◽  
Risk Premium ◽  
Equilibrium Model ◽  
Regime Switching ◽  
Yield Curve ◽  
Closed Form Solution ◽  
Form Solution ◽  
General Equilibrium Model

This paper develops a general equilibrium model of the term structure of interest rates in the presence of the systematic risk of regime shifts. The model elucidates the economic nature of the regime-shift risk premium and introduces a new source of time-variation in bond returns. A closed-form solution for the term structure of interest rates is obtained under an affine model using log-linear approximation. The model is estimated by Efficient Method of Moments. The regime-switching risk is found to be statistically significant and mostly affect the long-end of the yield curve.

Matrix product-form solutions for Markov chains with a tree structure

1994 ◽  
Vol 26 (4) ◽  
pp. 965-987 ◽  
Author(s):  
Raymond W. Yeung ◽  
Bhaskar Sengupta
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Closed Form Solution ◽  
Steady State Solution ◽  
Form Solution ◽  
Product Form ◽  
Matrix Product ◽  
Preemptive Resume ◽  
Finite Set ◽  
Markov Modulated

We have two aims in this paper. First, we generalize the well-known theory of matrix-geometric methods of Neuts to more complicated Markov chains. Second, we use the theory to solve a last-come-first-served queue with a generalized preemptive resume (LCFS-GPR) discipline. The structure of the Markov chain considered in this paper is one in which one of the variables can take values in a countable set, which is arranged in the form of a tree. The other variable takes values from a finite set. Each node of the tree can branch out into d other nodes. The steady-state solution of this Markov chain has a matrix product-form, which can be expressed as a function of d matrices Rl,· ··, Rd. We then use this theory to solve a multiclass LCFS-GPR queue, in which the service times have PH-distributions and arrivals are according to the Markov modulated Poisson process. In this discipline, when a customer's service is preempted in phase j (due to a new arrival), the resumption of service at a later time could take place in a phase which depends on j. We also obtain a closed form solution for the stationary distribution of an LCFS-GPR queue when the arrivals are Poisson. This result generalizes the known result on a LCFS preemptive resume queue, which can be obtained from Kelly's symmetric queue.

A new method for option pricing via time-fractional PDE

2018 ◽  
Vol 11 (05) ◽  
pp. 1850074 ◽  
Author(s):  
Elaheh Saberi ◽  
S. Reza Hejazi ◽  
Elham Dastranj
Keyword(s):  
Continuous Time ◽  
Regime Switching ◽  
Asset Price ◽  
Options Pricing ◽  
Chain Process ◽  
Hidden Markov Chain ◽  
Underlying Asset ◽  
Regime Switching Model ◽  
Switching Model ◽  
Fractional Pde

In this paper, power options pricing is driven via time-fractional PDE when the dynamic of underlying asset price follows a regime switching model in which the risky underlying asset depends on a continuous-time hidden Markov chain process. An exact solution for power options pricing is driven under our considered model.

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