Arbitrage Bounds for Prices of Weighted Variance Swaps

We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of co--maturing put options are given. We assume the given prices do not admit arbitrage and deduce no-arbitrage bounds on the weighted variance swap along with super- and sub- replicating strategies which enforce them. We find that market quotes for variance swaps are surprisingly close to the model-free lower bounds we determine. We solve the problem by transforming it into an analogous question for a European option with a convex payoff. The lower bound becomes a problem in semi-infinite linear programming which we solve in detail. The upper bound is explicit. We work in a model-independent and probability-free setup. In particular we use and extend F\"ollmer's pathwise stochastic calculus. Appropriate notions of arbitrage and admissibility are introduced. This allows us to establish the usual hedging relation between the variance swap and the 'log contract' and similar connections for weighted variance swaps. Our results take form of a FTAP: we show that the absence of (weak) arbitrage is equivalent to the existence of a classical model which reproduces the observed prices via risk-neutral expectations of discounted payoffs.Comment: 25 pages, 4 figure

Risk-sensitive investment in a finite-factor model

A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion maximisation problem in this setting. We provide an ODE for the optimal value function, which may be efficiently solved numerically. Relevant probability measure changes are discussed in the appendix. The approach of Klebaner and Lipster (2014) is used to prove the martingale property of the relevant density processes.Comment: 23 pages, 1 figur

Two Social Worlds: Social Correlates and Stability of Adolescent Status Groups

Examined adolescents\u27 peer group status in high school using self-report, peer nominations, and archival data collected during 2 consecutive school yrs. 408 students participated in the 1st yr, and 404 students participated in the 2nd yr. 60% of the 2nd yr Ss had also participated in the 1st yr. Higher status students (popular and controversial) had more close friends, engaged more frequently in peer activities, and self-disclosed more than lower status students (rejected and neglected). They were also more involved in extracurricular school activities and received more social honors from their schoolmates. Although the higher status students were more alike than different, controversial adolescents did report more self-disclosure and dating behavior than popular students. Lower status students were also highly similar, although rejected students reported lower grades

Complete-market models of stochastic volatility

In the Black–Scholes option-pricing theory, asset prices are modelled as geometric Brownian motion with a fixed volatility parameter σ, and option prices are deter-mined as functions of the underlying asset price. Options are in principle redundant in that their exercise values can be replicated by trading in the underlying. However, it is an empirical fact that the prices of exchange-traded options do not correspond to a fixed value of σ as the theory requires. This paper proposes a modelling framework in which certain options are non-redundant: these options and the underlying are modelled as autonomous financial assets, linked only by the boundary condition at exercise. A geometric condition is given, under which a complete market is obtained in this way, giving a consistent theory under which traded options as well as the underlying asset are used as hedging instruments

Coping With Cancer: Life Changes Reported by Patients and Significant Others Dealing with Leukemia and Lymphoma

http://deepblue.lib.umich.edu/bitstream/2027.42/51194/1/427.pd

Arrow Debreu Prices

Arrow Debreu prices are the prices of 'atomic' time and state contingent claims which deliver one unit of a specific consumption good if a specific uncertain state realizes at a specific future date. For instance, claims on the good 'ice cream tomorrow' are split into different commodities depending whether the weather will be good or bad, so that good-weather and bad-weather ice cream tomorrow can be traded separately. Such claims were introduced by K.J. Arrow and G. Debreu in their work on general equilibrium theory under uncertainty, to allow agents to exchange state and time contingent claims on goods. Thereby the general equilibrium problem with uncertainly can be reduced to a conventional one without uncertainty. In finite state financial models, Arrow-Debreu securities delivering one unit of the numeraire good can be viewed as natural atomic building blocks for all other state-time contingent financial claims; their prices determine a unique arbitrage-free price system