CMS, CMS SPREADS AND SIMILAR OPTIONS IN THE MULTI-FACTOR HJM FRAMEWORK

2012 ◽  
Vol 15 (07) ◽  
pp. 1250048
Author(s):  
PIERRE HANTON ◽  
MARC HENRARD
Keyword(s):  
Exact Solution ◽  
Previous Literature ◽  
Exact Equation ◽  
Gaussian Models ◽  
Market Models ◽  
Spread Options ◽  
Approximation Errors ◽  
Constant Maturity Swaps

Constant maturity swaps (CMS) and CMS spread options are analysed in the multi-factor HJM framework. For Gaussian models, which include a version of the Libor Market Models and the G2++ model, explicit approximated pricing formulae are provided. Two approximating approaches are proposed: an exact solution to an approximated equation and an approximated solution to the exact equation. The first approach borrows from previous literature on other models; the second approach is new. For the latter, the price approximation errors are smaller than in the previous literature and negligible in practice. These approaches are being used here to price standard CMS and CMS spreads and can be used for other European exotic products.

scholarly journals Pricing spread options under Levy jump-diffusion models

2021 ◽  
Author(s):  
Matthew Cane
Keyword(s):  
Stochastic Volatility ◽  
Strong Dependence ◽  
Computational Cost ◽  
Compound Poisson Process ◽  
Model Parameters ◽  
Option Prices ◽  
Market Models ◽  
Spread Options ◽  
Spread Option ◽  
Cir Process

This thesis examines the problem of pricing spread options under market models with jumps driven by a Compound Poisson Process and stochastic volatility in the form of a CIR process. Extending the work of Dempster and Hong, and Bates, we derive the characteristic function for two market models featuring normally distributed jumps, stochastic volatility, and two different dependence structures. Applying the method of Hurd and Zhou we use the Fast Fourier Transform to compute accurate spread option prices across a variety of strikes and initial price vectors at a very low computational cost when compared to Monte-Carlo pricing methods. We also examine the sensitivities to the model parameters and find strong dependence on the selection of the jump and stochastic volatility parameters.

scholarly journals From P/E Ratio to Fuzzy Infinite Spreadsheet—Mathematically Rigorous Derivations of the Zeroth and the First Order Solutions of Rate of Return

2022 ◽  
Vol 5 (1) ◽  
pp. p7
Author(s):  
Hugh Ching (USA) ◽  
Chien Yi Lee (China) ◽  
Benjamin Li (Canada)
Keyword(s):  
Exact Solution ◽  
Real Estate ◽  
Initial Conditions ◽  
Investment Analysis ◽  
Rate Of Return ◽  
Exact Equation ◽  
Zeroth Order ◽  
Real Estate Investment ◽  
First Order ◽  
Order Solution

The P/E Ratio (Price/Earning) is one of the most popular concepts in stock analysis, yet its exact interpretation is lacking. Most stock investors know the P/E Ratio as a financial indicator with the useful characteristics of being relatively time-invariant. In this paper, a rigorous mathematical derivation of the P/E Ratio is presented. The derivation shows that, in addition to its assumptions, the P/E Ratio can be considered the zeroth order solution to the rate of return on investment. The commonly used concept of the Capitalization Rate (Cap Rate = Net Income / Price) in real estate investment analysis      can also be similarly derived as the zeroth order solution of the rate of return on real estate investment. This paper also derives the first order solution to the rate of return (Return = Dividend/Price + Growth) with its assumptions. Both the zeroth and the first order solutions are derived from the exact future accounting equation (Cash Return = Sum of Cash Flow + Cash from Resale). The exact equation has been used in the derivation of the exact solution of the rate of return. Empirically, as an illustration of an actual case, the rates of return are 3%, 73%, and 115% for a stock with 70% growth rate for, respectively, the zeroth order, the first order, and the exact solution to the rate of return; the stock doubled its price in 2004. This paper concludes that the zero-th, the first order, and the exact solution of the rate of return all can be derived mathematically from the same exact equation, which, thus, forms a rigorous mathematical foundation for investment analysis, and that the low order solutions have the very practical use in providing the analytically calculated initial conditions for the iterative numerical calculation for the exact solution. The solution of value belongs to recently classified Culture Level Quotient CLQ = 10 and is in the process of being updated by fuzzy logic with its range of tolerance for predicting market crashes to advance to CLQ = 2.

scholarly journals Duality theory under model uncertainty for non-concave utility functions

2019 ◽  
pp. 50-56
Author(s):  
O. O. Kharytonova
Keyword(s):  
Probabilistic Model ◽  
Model Uncertainty ◽  
Duality Theory ◽  
Utility Maximization ◽  
Utility Functions ◽  
Previous Literature ◽  
Market Models ◽  
Terminal Wealth ◽  
Complete Market ◽  
Robust Utility Maximization

The main goal for this paper is to study the robust utility maximization functional, i.e. sup_{X\in\Xi(x)} inf_{Q\in\mathsf{Q}} E_Q [U(X_T)]; of the terminal wealth in complete market models, when the investor is uncertain about the underlying probabilistic model and averse against both risk and model uncertainty. In the previous literature, this problem was studied for strictly concave utility functions and we extended existing results for non-concave utility functions by considering their concavization.

scholarly journals Pricing spread options under Levy jump-diffusion models

2021 ◽  
Author(s):  
Matthew Cane
Keyword(s):  
Stochastic Volatility ◽  
Strong Dependence ◽  
Computational Cost ◽  
Compound Poisson Process ◽  
Model Parameters ◽  
Option Prices ◽  
Market Models ◽  
Spread Options ◽  
Spread Option ◽  
Cir Process

This thesis examines the problem of pricing spread options under market models with jumps driven by a Compound Poisson Process and stochastic volatility in the form of a CIR process. Extending the work of Dempster and Hong, and Bates, we derive the characteristic function for two market models featuring normally distributed jumps, stochastic volatility, and two different dependence structures. Applying the method of Hurd and Zhou we use the Fast Fourier Transform to compute accurate spread option prices across a variety of strikes and initial price vectors at a very low computational cost when compared to Monte-Carlo pricing methods. We also examine the sensitivities to the model parameters and find strong dependence on the selection of the jump and stochastic volatility parameters.

scholarly journals Superconvergence Analysis of Finite Element Method for a Second-Type Variational Inequality

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Dongyang Shi ◽  
Hongbo Guan ◽  
Xiaofei Guan
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Variational Inequality ◽  
Theoretical Analysis ◽  
Error Estimate ◽  
Numerical Results ◽  
Previous Literature ◽  
Superconvergence Results ◽  
Norm Error

This paper studies the finite element (FE) approximation to a second-type variational inequality. The supe rclose and superconvergence results are obtained for conforming bilinear FE and nonconformingEQrotFE schemes under a reasonable regularity of the exact solutionu∈H5/2(Ω), which seem to be never discovered in the previous literature. The optimalL2-norm error estimate is also derived forEQrotFE. At last, some numerical results are provided to verify the theoretical analysis.

PRICING CMS SPREAD OPTIONS IN A LIBOR MARKET MODEL

2010 ◽  
Vol 13 (01) ◽  
pp. 45-62 ◽  
Author(s):  
DENIS BELOMESTNY ◽  
ANASTASIA KOLODKO ◽  
JOHN SCHOENMAKERS
Keyword(s):  
Numerical Study ◽  
Market Model ◽  
Approximation Methods ◽  
Option Prices ◽  
Model Assumption ◽  
Market Models ◽  
Libor Market Model ◽  
Spread Options ◽  
Swap Model ◽  
Spread Option

We present two approximation methods for the pricing of CMS spread options in Libor market models. Both approaches are based on approximating the underlying swap rates with lognormal processes under suitable measures. The first method is derived straightforwardly from the Libor market model. The second one uses a convexity adjustment technique under a linear swap model assumption. A numerical study demonstrates that both methods provide satisfactory approximations of spread option prices and can be used for calibration of a Libor market model to the CMS spread option market.

The exact equation for Brillouin shifts

1965 ◽  
Vol 26 (11) ◽  
pp. 655-658 ◽  
Author(s):  
V. Chandrasekharan
Keyword(s):  
Exact Equation

Exact solution of a four-site crystal model for an intermediate-valence system

1986 ◽  
Vol 47 (6) ◽  
pp. 1029-1034 ◽  
Author(s):  
J.C. Parlebas ◽  
R.H. Victora ◽  
L.M. Falicov
Keyword(s):  
Exact Solution ◽  
Intermediate Valence ◽  
Crystal Model
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