My thesis (and the associated tools) naturally builds on itself as the chapters progress. This is because each subsequent article was an extension of the previous. In Chapter 2, we identified regulatory and subsidy policy uncertainty as a primary area of future research. This was the subject of our second article in Chapter 3. In the second article, we identified the bandwidth of the best and worst case prices as being too large and that perhaps utility indifference may be a better tool to address model uncertainty. In our next article in Chapter 4, already aware of the shortcomings of
the superhedging and subhedging prices, we employed a utility indifference approach to generate the bid-ask prices. In Chapter 4, we also identify areas of future research for ourselves and interested readers.
Our model in Chapter 3 can be extended on several fronts. To improve the model, more classes of jump distributions or non-constant (in fact, possibly stochastic) Pois- son arrival rates could be considered for future work. Another possible improvement to the expected subsidy jump model would be to incorporate management’s views on the probability of possible policy outcomes or cases, each with an associated proba- bility determined by management. Beyond the worst case pricing scenario, we could consider the whole space of equivalent martingale measures and seek a pricing measure following the ambiguity aversion methodsv(x,0) = supαinfQE[U(XT, T) +κh(Q|P)]
whereU is the utility of terminal wealthXT,P is the estimated jump diffusion mea-
sure, Qis another possible measure from our uncertain parameter bounds, andhis a penalty function that penalizes choices Q different from P, with associated ambigu- ity aversion parameter κ. We note that the worst case measure and pricing equation associated with our method follows from the aversion parameter approaching zero κ= 0 and the risk neutral utility function U(X) =X. This would be an application of utility based pricing. Further still, one could try to hedge the policy risk factor with some sort of correlated asset using a utility indifference pricing approach. Different possible hedging targets could be chosen such as exponential utility or a global mean variance technique.
In Chapter 4, we identified many possible extensions and additional applications of our model. One could investigate whether the presence of permanent price impact may allow the market maker to manipulate the derivative price and to what extent price manipulation may be mitigated with Asian style options. Our market impact model can be used when hedging in distressed markets like, for example, during the financial crisis of 2007 where liquidity in the markets dried up dramatically. Rather than building the impact parameters on a single current snapshot in time, to reflect future liquidity risk, one might use a “term structure of illiquidity.” This could be based on an index, futures, or analyst estimates and the parameters could be time varying and possibly stochastic. The model can also be applied in daily market mak- ing such as market microstructure models. It is possible to choose impact functions that better reflect the limit order book structure on exchanges or electronic broker- dealer networks. Our framework is sufficiently general that it can be incorporated into a more general market making framework such as managing inventory risk or optimal liquidation. It is possible to price American style options within our framework and
we presented the associated HJB equations for future research. Lastly we suggest the relatively simple extension of multi-asset options, which is a straightforward exten- sion of the HJB equation. Additionally, we believe a sound pricing framework should better account for opportunity cost in the indifference price. We suggest for future research the consideration that the agent in his portfolio optimization may also be allowed to hedge with some sort of market index ETF.
Christian Maxwell
Education
PhD in Applied Mathematics: Financial Mathematics 2015 University of Western Ontario
BASc in Engineering Science: Aerospace Engineering 2008 University of Toronto
Work and Volunteer History
Quantitative Associate 2014–Present BMO Capital Markets
Toronto, ON
Summer Associate 2013
CIBC Risk Management Toronto, ON
Lecturer 2012
Western University London, ON
Senior Analyst 2009–2010
Ernst & Young LLP Toronto, ON
Incident Manager 2008
Virgin Mobile Toronto, ON
Volunteer 2008
University of Toronto Centre for International Health (CIH) Kep, Cambodia
Program Coordinator 2007
University of Toronto, Science Outreach Toronto, ON
Camp Counselor 2006
University of Toronto, Science Outreach Toronto, ON
Christian Maxwell
Extracurricular Activities
SIAM Student Chapter Executive 2013
PRMIA Toronto Risk Management Case Competition 2012 University of Western Ontario Student Development Centre Peer Advisor 2010–2012 TEDxUTIHP Volunteer and Event Photographer 2011 University of Toronto Health and Human Rights Conference Volunteer 2009–2010
Scarborough Sharks Hockey Volunteer 2008–2009
U of T Centre for International Health Cambodia Project 2008 Chair of the Engineering Science Club 2007–2008
Relevant Works and Papers
PhD Thesis: Applications of Stochastic Control to Energy Real Options and Market Illiq- uidity. 2014.
Working Paper: Maxwell, C and Davison, M. Optimal Hedging in Illiquid Markets. 2014. Working Paper.
Accepted Article: Maxwell, C and Davison, M. Real Options with Regulatory Policy Uncertainty. 2014. Fields Special Volume.
Published Article: Maxwell, C and Davison, M. Using Real Option Analysis to Quantify Ethanol Policy Impact on the Firm’s Entry into and Optimal Operation of Corn Ethanol Facilities. 2013. Energy Economics.
BASc Thesis: The Propulsive Performance of Ramrockets at Lift-off.