REAL SWITCHING OPTIONS I BEST OF TWO OUTPUTS II

Transcript:REAL SWITCHING OPTIONS I BEST OF TWO OUTPUTS II:
REAL SWITCHING OPTIONS I BEST OF TWO OUTPUTS II STOCHASTIC INPUT AND OUTPUT: OPTION TO SHUT DOWN, OPTION TO RESTART III LOWEST COST OF TWO INPUTS 1 Real Options 2015 2 General Switching Options Flexibility has significant value in certain markets, especially for correlation < 1 Adkins and Paxson (2012) Trigeorgis and Mason (1987) Deterministic models unable to capture this option value Model as an exchange option, but need dimension reducing transformation Quasi-analytical solution for multi-factor models Brennan and Schwartz (1985), Paxson (2005) One-factor models Margrabe (1978), McDonald and Siegel (1985), Paxson and Pinto (2005) Ignore the switching costs He and Pindyck (1992), Brekke and Schieldrop (2000) Real Options 2015 I General Output Switching EXAMPLES: SHIP COMBINATION CARRIERS=EITHER WET OR DRY CARGO REAL ESTATE=EITHER RESIDENTIAL OR OFFICE TENANTS FINANCE CLASSES=EITHER REAL OPTIONS OR INVESTMENT ANALYSIS ELECTIVES FINANCE CAREER CHOICE=EITHER ACADEMIA OR CONSULTING OR BUSINESS Real Options 2015 3 OUTPUT SWITCHES Sødal et al. 2008 SHIPPING SWITCHES Real Options 2015 4 Sell Ammonia or Use to Produce Urea? Real Options 2015 5 SINGLE ONE-WAY SWITCHING Real Options 2015 6 SINGLE OUTPUT SWITCH Real Options 2015 7 VM & SP CONDITIONS Real Options 2015 8 9 Real Options 2015 II SUSPENSION & RESTART OPTIONS 19th Century Manchester Real Options 2015 10 11 (OUTPUT-INPUT) SWITCHES NAT GAS AS INPUT FOR PRODUCING CRUDE OIL, ALBERTA, or ALTERNATIVELY, OUTPUT SWITCHES FOR NORWAY PETRO Real Options 2015 EUROPEAN OIL REFINERIES Real Options 2015 12 Two-factor Switching Model Input price follows gBm 13 Output price follows gBm Convenience yield for output / input Volatility for output / input Correlation Required return on output / input Value of asset in state 2 Value of asset in state 1 Inactive suspended state denoted by 2 Active operating state denoted by 1 Real Options 2015 Two-factor Switching Model 14 RNVR for state 2: Solution: with characteristic root equation: RNVR for state 1: Solution: with characteristic root equation: Real Options 2015 Two-factor Switching Model 15 Economic conditions favour a switch from inactive to active state when input price is low when output price is high, and Economic conditions favour a switch from active to inactive state when input price is high when output price is low, and Real Options 2015 16 Two-factor Switching Model Switching cost from state 2 to state 1 Switching cost from state 1 to state 2 Optimality conditions Value matching switching Real Options 2015 17 Two-factor Switching