Markets, profits, capital, leverage and return

Peter Carr, Dilip B. Madan, Juan Jose Vicente Alvarez

Research output: Contribution to journalArticle

Abstract

Cherny and Madan’s theory of two-price markets yields closed forms for bid and ask prices. By defining profits as the difference between the mid quote and the risk-neutral expectation, and capital as the difference between the ask and bid prices, we obtain precise expressions for profit, capital and, hence, return. New expressions are developed for the bid and ask prices in terms of the sensitivity of the inverse distribution function to the quantile level. The latter turns out to be a measure of risk exposure at the quantile level. The theory is illustrated on unhedged exposures in the Black-Scholes-Merton model, followed by variance swaps and call options for variance gamma underliers. It is argued that markets should economize capital and, furthermore, that the maximization of expected utility may involve an uneconomic use of capital. We further observe that stock positions should be revised downward from zero delta in left-skewed markets in response to the target gamma when minimizing capital commitments.

Original languageEnglish (US)
Pages (from-to)95-122
Number of pages28
JournalJournal of Risk
Volume14
Issue number1
StatePublished - Sep 1 2011

Fingerprint

Leverage
Profit
Bid
Quantile
Market price
Distribution function
Black-Scholes
Measure of risk
Call option
Variance swap
Risk exposure
Expected utility
Variance gamma
Merton model

ASJC Scopus subject areas

  • Strategy and Management
  • Finance

Cite this

Carr, P., Madan, D. B., & Alvarez, J. J. V. (2011). Markets, profits, capital, leverage and return. Journal of Risk, 14(1), 95-122.

Markets, profits, capital, leverage and return. / Carr, Peter; Madan, Dilip B.; Alvarez, Juan Jose Vicente.

In: Journal of Risk, Vol. 14, No. 1, 01.09.2011, p. 95-122.

Research output: Contribution to journalArticle

Carr, P, Madan, DB & Alvarez, JJV 2011, 'Markets, profits, capital, leverage and return', Journal of Risk, vol. 14, no. 1, pp. 95-122.
Carr P, Madan DB, Alvarez JJV. Markets, profits, capital, leverage and return. Journal of Risk. 2011 Sep 1;14(1):95-122.
Carr, Peter ; Madan, Dilip B. ; Alvarez, Juan Jose Vicente. / Markets, profits, capital, leverage and return. In: Journal of Risk. 2011 ; Vol. 14, No. 1. pp. 95-122.
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