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Summer Term 2015/16

Venue: A1.01. Fridays @2pm in Weeks 5,6,9,10 (May 27, June 3, June 24, July 1)

The topic for this term is Term structure models and we will be working from the book Term-Structure Models: A graduate course (2009), Springer Finance Textbook by Damir Filipovic.

Dominic Norgilas will speak about Short Rate models on Friday 27th May.

Spring Term 2015/16

Venue: Fridays 2-3pm in C1.06 (except week 1 in H0.58)

Week 10: Friday 18th March - Matthew Burgess (Statistics) - Modelling Investor Activity Levels

Week 9: Friday 11 March - Vicky Henderson (Statistics) - The Value of Being Lucky: Option Backdating and Non-Diversifiable Risk

Week 6: Friday 19th February - Yufan Zhao (Statistics) - Optimal stopping under the BNS model

The BNS model is a stochastic volatility model where the leverage effect in the market is modelled by a correlated jump term between volatility and the asset price. We studied the properties of the American options under this model and highlights some of the difficulties caused by the jump term in the model.

Week 4: Fri 5th February - Alex Tse (Statistics) - Variants of contracting models

I will give a brief and selective overview of contract theory, which deals with the problem of how a principal should set out incentives with an agent in order to optimise certain economic objectives. Two types of problem will be introduced. In a moral hazard problem, agent's actions are unobservable and thus a principal has to use a suitable contract to induce the agent to undertake certain actions in favour of the output value growth. In an employee compensation problem, a principal seeks a minimal cost contract acceptable by the agent. I will discuss some recent results featuring probability weighting which could justify the industrial practice of granting option-like payoffs to employees.

Week 3: Fri 29th January - Seb Armstrong (Statistics) - On representing and hedging claims for coherent risk measures

In this talk we'll introduce coherent risk measures, and then consider the problem of reserving for claims in multiple numeraires in discrete time, under a coherent risk measure, with a view to updating the capital requirement dynamically. To this end, we generalise established notions of time-consistency, representability, and m-stability, for a finite collection of numeraires V.

Autumn Term 2015/16

Venue: Fridays @2pm in C1.06

Week 3: Fri 23rd October - Zhun Liu (WBS) - One approximation of real-world corporate financing decisions

This paper is the first attempt to reconcile the prospect theory and the contract theory in explaining the observed financing decisions. In a world of ambitious and aggressive economic agents, even the original equilibria under the presence of asymmetric information break down. When the aggressiveness in the market is prevailing, there exist multi-pooling-equilibria, which might help explain why the academic can not find the optimal leverage. In the mean- while, debt issuance would be lower, which shed light on the distinct liquidity provision patterns between bull and bear market. Firm with lottery-like in- vestment opportunity will more easily get external financing than that with safe project, as both market participants, entrepreneur and financier, perceive the project more valuable than the value would otherwise be suggested by the classical expected utility theory.

Week 4: Alex Tse (Statistics) An introduction to realization utility and a few related optimal stopping models.

Week 7: Jun Maeda (Statistics) A Stochastic Volatility Model with a Focus on Autocallables

In order to meet with clients' request, banks are forced to price various
exotic products. Generally, we cannot price them 'correctly' with the ordinary
Black-Scholes model. Instead, the banks use some kind of stochastic volatility model.
We try to enhance one of the models, the Heston model, to take into account
an additional factor, supply and demand of the volatility, for the traders to
value/hedge better their portfolios. We focus especially in the Japanese volatility market where the presenter has
experience in trading.

Week 8: Mingliang Cheng (WBS) - Corporate valuation and optimal operation under liquidity constraints

We investigate the impact of cash reserves upon the optimal behaviour of a modelled firm that has uncertain future revenues. To achieve this, we build up a corporate financing model of a firm from a Real Options foundation, with the option to close as a core business decision maintained throughout. We model the firm by employing an optimal stochastic control mathematical approach, which is based upon a partial differential equations perspective. In so doing, we are able to assess the incremental impacts upon the optimal operation of the cash constrained firm, by sequentially including: an optimal dividend distribution; optimal equity financing; and optimal debt financing (conducted in a novel equilibrium setting between firm and creditor). We present efficient numerical schemes to solve these models, which are generally built from the Projected Successive Over Relaxation (PSOR) method, and the Semi-Lagrangian approach. Using these numerical tools, and our gained economic insights, we then allow the firm the option to also expand the operation, so they may also take advantage of favourable economic conditions.