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Abstract
As traditional contingent claims valuation methods do not apply to non-transferable and non-hedgeable contingent claims, recent proliferation of such claims creates the need for the development of new valuation methods. Further, the essential role of executive stock options (henceforth ESOs) in current economic system makes their valuation a necessity for optimally allocating resources and incentivizing executives.
In this thesis, I offer a novel method of valuating non-transferable, non-hedgeable (henceforth NTNH) contingent claims and then implement this method in pricing ESOs. I find that NTNH constraints break the local co-linearity caused by including contingent claims in solving the portfolio optimization problems. Thus, I am able to translate the portfolios that include contingent claims optimization problems into primary assets only portfolios optimization problems, by replicating contingent claims using primary assets. I integrate the NTNH constraints into one single rectangular constraint, under which solving the portfolio optimization problem identifies the pricing stochastic discount factor. I then use this stochastic discount factor to price the NTNH contingent claims and implement the method in pricing ESOs. I investigate both block exercise and continuous partial exercise, and derive the first order conditions with respect to optimal exercise rates for continuous partial exercise case. The priced assets could also be pensions, human capital, real estate, etc.
I also address default NTNH contingent claim valuation. I extend the above model by introducing default primary assets which help replicating default contingent claims. Again, I derive a stochastic discount factor to price the default NTNH contingent claims. I implement the valuation method in pricing ESOs with job termination.
Finally, I apply NTNH contingent claims valuation method to reload options pricing, again, by replication, solving portfolio optimization problems, and identifying the appropriate stochastic discount factor. I start in an unconstrained setting and find that as the frequency of reload increases the optimal reload policy evolves from an optimal stopping time into a barrier hitting time. The barrier is the historically high price, and the number of replicating shares converges. As the mature- stock-for-strike convention being added into the reload option exercise policy, if the vesting period for stock and option are optimally chosen, then the option quality measure, the incentive per unit dead weight cost will be increased.