Mini-Workshop on Mathematical Finance

Monday May 20th 2019
Adam Smith Business School

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General admission
Free + £0.00 fees


10.00 - 10.30: Welcome and coffee

10.30 - 12.30: Session 1 featuring Professor Peter Carr and Professor Svetlana Boyarchenko

12.30 - 13.30: Lunch

13.30 - 15.30: Session 2 featuring Dr Ankush Agarwal and Professor Christian Ewald

Session 1:

Professor Peter Carr, New York University

'Just-in-time Portfolio Insurance'

Conventional portfolio insurance places a floor on the value of a portfolio relative to its value at inception. Just-in-time portfolio insurance instead places a floor on the value of a portfolio relative to its value on the previous day. The owner of a just-in-time insured portfolio can floor any daily price relative just after it is realized. The owner can also choose not to floor any daily price relatives and hence receive the value appreciation over the term of the contract. Dynamic programming (DP) can be used to value the Bermudan optionality embedded in a just-in-time insured portfolio. We apply DP using both the benchmark Black Scholes model and a new approach based on abstract algebra. The latter approach leads to a simple arbitrage-free closed-form valuation formula for our Bermudan-style insurance.

Professor Svetlana Boyarchenko, University of Texas at Austin

'Static and Semi-Static Hedging as Contrarian or Conformist Bets'

In this paper, we argue that, once the costs of maintaining the hedging portfolio are properly taken into account, semi-static portfolios should more properly be thought of as separate classes of derivatives, with non-trivial, model-dependent payoff structures. We derive new integral representations for payoffs of exotic European options in terms of payoffs of vanillas, different from Carr-Madan representation, and suggest approximations of the idealized static hedging/replicating portfolio using vanillas available in the market. We study the dependence of the hedging error on a model used for pricing and show that the variance of the hedging errors of static hedging portfolios can be sizably larger than the errors of variance-minimizing portfolios. We explain why the exact semi-static hedging of barrier options is impossible for processes with jumps, and derive general formulas for variance-minimizing semi-static portfolio. We show that hedging using vanillas only leads to larger errors than hedging using vanillas and first touch digitals. In all cases, efficient calculations of the weights of the hedging portfolios are in the dual space using new efficient numerical methods for calculation of the Wiener-Hopf factors and Laplace-Fourier inversion.

Session 2:

Dr Ankush Agarwal, Adam Smith Business School

'Implied Sharpe ratio in incomplete markets'

In the financial markets, European calls and puts are usually compared based on their implied volatilities. While implied volatility provides an idea about the price of an option, it does not provide any measure of its worth to an investor who is looking to maximise her utility. In this work, we introduce the implied Sharpe ratio which rectifies this shortcoming by providing a measure which could be used to compare different European options for investment purposes. We study implied Sharpe ratio in the context of incomplete market models. In the absence of closed-form formulas of implied Sharpe ratio, we use the coefficient expansion technique developed by Lorig et al. (2017) to find semi-explicit approximation in terms of the risk-aversion parameter and other model parameters.

Professor Christian Ewald, Adam Smith Business School

'Real Options, Risk Aversion and Markets'

We analyze the effect of risk aversion and the presence of financial markets on the optimal exercise of real options. Using value matching and smooth pasting conditions, we generalize results of Sodal and Shackleton (2005) for the one-dimensional complete market case and extend their framework to a multi-dimensional incomplete market setup, identifying the minimal martingale measure as the appropriate reference measure, which is consistent with the Capital Asset Pricing Model (CAPM). Further, we look at so called myopic look-ahead rules within the context of financial markets and of the CAPM in particular and provide a characterization of the optimal exercise rule in terms of the capital market line of CAPM. Finally we demonstrate via numerical examples that it is crucial to take these aspects of financial markets into account when exercising real options, as otherwise large financial losses can occur.

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Starts: Monday, May 20th 2019 at 10:00am
Ends: Monday, May 20th 2019 at 3:30pm

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Timezone: Europe/London
Bookings close: May 17th 2019


Adam Smith Business School
University of Glasgow
Main Building Lecture Theatre 206

G12 8QQ
United Kingdom

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This event is organized by Adam Smith Business School.

Telephone 0141 330 3429
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