Topics in Derivatives/MSc-Seminar Derivate

Transcription

1 in Derivatives/MSc-Seminar Derivate Prof. Dr. Alexander Szimayer Chair of Derivatives Summer Term 2014 Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13

2 Overview Contents: studying an advanced topic in derivatives: option pricing dependence modeling risk management writing of a term paper Target Audience: MSc students in Economics, Business Administration, Wirtschaftsmathematik, Wirtschaftsingenieurwesen Prerequisites: advanced course on derivatives, e.g., Derivatives: Pricing and Hedging (MSc course, winter term 2013/14) in case this prerequisite is not met, please attend the course Continuous Time Finance (MSc course, summer term 2014) Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13

3 Overview Lecturer in Charge/ Prof. Dr. Alexander Szimayer Supervisors: Michael Herbener Konstantin Neinstell Benjamin Nyarko Sebastian Opitz Henry Seidel Rainer Volk Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13

4 Overview Important Dates: April 1, 2014, 16-18, WiWi tba: introduction of topics students select their preferred topics April 2, 2014, 14-20, WiWi tba: 14-17, introduction of methods, software and data marts 17-20, how to write a term paper Jun 16, 2014, 12 Uhr: handing in of term paper June 20/21, 2014, WiWi tba: June 20, 2014, 8-18: talk by students (part 1) June 21, 2014, 8-18: talk by students (part 2) Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13

5 Overview Schedule: students hand in their list of preferred topics by April 1, 2014 students receive their final topic and supervisor by April 2, 2014 students schedule appointments with their supervisors (usually 2 to 3 appointments) students take minutes of each appointment Additional Resources: See follow the link Lehre, then Wissenschaftliches Arbeiten Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13

6 1. Lévy-Processes: Variance Gamma (VG): Black-Scholes cannot explain volatility smiles and smirks observed in option markets. Alternatives to Black-Scholes include models that preserve the structural properties of the original model (such as iid increments of log-prices) however, with an additional jump component. Thus, the Wiener process as driver of the stock price is replaced by the more general class of Lévy processes. The aim is to introduce this model class by studying the variance gamma (VG) process using Monte Carlo methods, and potentially also Fourier methods, both, for the purpose of option pricing. Prof. Dr. Alexander Szimayer Madan, D., Carr, P., Chang, E. (1998) The Variance Gamma Process and Option Pricing. In: European Finance Review 2: Fu, M.C. (2000) Variance-Gamma and Monte Carlo. In Fu, M.C., Jarrow, R.A., Yen, J.J, Elliott, R.J. (Eds) Advances in Mathematical Finance. Boston, Birkhauser. Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13

7 2. The Heston-Model and Its Discretization: Black-Scholes cannot explain volatility smiles and smirks observed in option markets. To accommodate this effect, the model of Heston (1993) is widely used in practice. In the Heston model the volatility is no longer constant but evolves randomly over time. The aim is to address Heston by Monte Carlo methods using a discretization scheme proposed by Broadie und Kaya (2006). In particular, the Broadie-Kaya scheme has to be implemented and compared to standard methods, e.g., Euler and Milstein, regarding error and convergence rate. Konstatin Neinstell Broadie, M., and Kaya, Ö. (2006) Exact simulation of stochastic volatility and other affine jump diffusion processes. In: Operations Research 54(2): Van Haastrecht, A., and Pelsser, A. (2010) Efficient, almost exact simulation of the Heston stochastic volatility model. In: International Journal of Theoretical and Applied Finance 13(1): Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13

8 3. Heston Trees: In the scientific world it is well known that some assumptions of the Black Scholes model can t be proven empirically. The assumption of log-normal distributed returns with constant volatility leads to biased option prices. With the following extension to the classic Black Scholes model, Heston (1993) offers another approach based on stochastic volatility: dv t = κ(v t v)dt + φ(v t)dw 1 t ds t = ν(v t)s tdt + ψ(v t)s tdw 2 t, where W 1 and W 2 are stochastic processes with a constant correlation ρ on a complete probability space (Ω, F, P). κ, θ and η are constant parameters. Although there is a (semi-)closed solution for plain vanilla options, exotic options e.g. American options need to be priced numerically. Beliaeva and Nawalkha (2010) present a discrete scheme which is based on path-dependent trees and excels in accuracy and efficiency. Work on the scheme analytically and numerically and implement the model if applicable. Compare the scheme to alternatives e.g. Leisen (2000). Benjamin Nyarko Beliaeva, N., and Nawalkha S.K. (2010) A simple Approach to Pricing American Options Under the Heston Stochastic Volatility Model. In: Journal of Derivatives 17(4): Leisen, D. (2000) Stock Evolution under Stochastic Volatility: A Discrete Approach. In: Journal of Derivatives 8(2): 9-27 Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13

9 4. Copulas and Financial Data Analysis: Recent analysis on the dependence of different asset classes called into question the assumption of normality for the joint distribution of asset returns. More flexibility in modeling the dependence structure is provided by the copula approach. The aim of the seminar work is to investigate the bivariate dependence structure of different asset classes using one-parameter families of Archimedean copulas. Sebastian Opitz Ané, T., and Kharoubi C. (2003) Dependence structure and risk management. In: The Journal of Business 76(3): Joe, H. (1997) Multivariate Models and Dependence Concepts, chapter 5. Nelsen, R.B. (2006) An Introduction to Copulas, chapter 2 & 4 Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13

10 5. Minimum-Variance Hedging of Second-Hand Ship Values: Ship owners are exposed to risk of highly volatile ship prices. As of today there is no liquid derivative instrument to hedge these values directly. Therefore Alizadeh & Nomikos (2012) propose a cross-hedge using freight derivatives. The aim of this work to check the performance of such a strategy on real sales values of second-hand vessels. Henry Seidel Alizadeh, A.H., and Nomikos, N. K. (2012) Ship finance: Hedging ship price risk using freight derivatives. In: W. K. Talley, ed., The Blackwell Companion To Maritime Economics, 1st ed., Wiley-Blackwell, West Sussex, chapter 22 Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13

11 6. Trading Strategies in the Market for Merchant Ships: The sale and purchase market for merchant ships is characterized by high volatility and heavily depends on the development of the underlying earnings of operating the ship (e.g., freight rates). Consequently, shipowners and investors face difficult decisions on investment and divestment timing for merchant ships. Within other financial markets, fundamental and technical analyses are widely-used to develop trading strategies that yield excess returns compared to the classical buy-and-hold strategy. It shall be investigated whether this can be successfully implemented in the sale and purchase market for merchant ships. Touched methods/concepts: co-integration techniques VECM models moving average trading strategies (if necessary: bootstrapping) Data: Historical ship prices and freight rates for different tanker and dry-bulk ship classes can be obtained from Clarksons Shipping Intelligence Network (SIN). Michael Herbener Alizadeh, A.H., and Nomikos, N.K. (2006) Trading strategies in the market for tankers. In: Maritime Policy and Management 33(2): Alizadeh, A.H., and Nomikos, N.K. (2007) Investment timing and trading strategies in the sale and purchase market for ships. In: Transportation Research Part B, 41(1): Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13

12 7. Merton s Portfolio Problem: The aim of this seminar paper is to present one of the most famous applications of stochastic optimal control in economics. The portfolio problem of Robert C. Merton addresses the question how an investor allocates his wealth and controls his consumption in order to maximize expected utility. Basic knowledge of stochastic calculus or dynamic programming is recommended. Rainer Volk Merton, R.C. (1969) Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case. In: The Review of Economics and Statistics 51(3): Björk, T. (2009) Arbitrage Theory in Continuous Time (Oxford Finance) (third edition), Chapter 19 Merton, R.C. (1971) Optimum Consumption and Portfolio Rules in a Continuous-Time Model. In: Journal of Economic Theory 3(4): Merton, R.C. (1992) Continuous-Time Finance, chapter 4 Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13

13 8. Propose your own Topic In case you are interested in a particular topic not included in the given list, you can propose your own topic by writing a one-page proposal and send it to derivate@wiso.uni-hamburg.de Re: Topics in Derivatives/MSc-Seminar Derivate. no later than March 31, 2014, noon. We let you know as soon as possible, whether we can accommodate your suggestion. will be assigned accordingly Prof. Dr. Alexander Szimayer (UHH) Topics in Derivatives/MSc-Seminar Derivate Summer Term / 13