Agarwal, Ankush; Lorig, Matthew The implied Sharpe ratio. (English) Zbl 1454.91274 Quant. Finance 20, No. 6, 1009-1026 (2020). The authors introduce a new concept – the implied Sharpe ratio – which allows investors to compare various European options: the option with the highest implied Sharpe ratio, if included in an investor’s portfolio, will improve his expected utility the most. Through the method of Taylor series expansion of the state-dependent coefficients in a nonlinear partial differential equation, they also establish the behaviour of the implied Sharpe ratio with respect to an investor’s risk-aversion parameter. In a series of numerical studies, they compare the investment attractiveness of different European options by studying their implied Sharpe ratio. Reviewer: George Stoica (Saint John) MSC: 91G20 Derivative securities (option pricing, hedging, etc.) 91G10 Portfolio theory Keywords:Sharpe ratio; PDE asymptotics; stochastic volatility; Heston; reciprocal Heston PDFBibTeX XMLCite \textit{A. Agarwal} and \textit{M. Lorig}, Quant. Finance 20, No. 6, 1009--1026 (2020; Zbl 1454.91274) Full Text: DOI arXiv Link References: [1] Carmona, R., Indifference Pricing: Theory and Applications, 2008 (Princeton University Press: Princeton, NJ). [2] Delbaen, F. and Schachermayer, W., The Mathematics of Arbitrage, 2006 (Springer Science & Business Media: Berlin). · Zbl 1106.91031 [3] Duffee, G.R., Term premia and interest rate forecasts in affine models. J. Finance, 2002, 57(1), 405-443. doi: 10.1111/1540-6261.00426 [4] Eeckhoudt, L., Gollier, C. and Schlesinger, H., The risk-averse (and prudent) newsboy. Manage. Sci., 1995, 41(5), 786-794. doi: 10.1287/mnsc.41.5.786 · Zbl 0843.90036 [5] Follmer, H. and Schweizer, M., Hedging of contingent claims. Appl. Stoch. Anal., 1991, 5, 389. · Zbl 0738.90007 [6] Friedman, A., Partial Differential Equations of Parabolic Type, 2008 (Courier Dover: Mineola, NY). [7] Heston, S.L., A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud., 1993, 6(2), 327-343. doi: 10.1093/rfs/6.2.327 · Zbl 1384.35131 [8] Hodges, S.D. and Neuberger, A., Optimal replication of contingent claims under transaction costs. Rev. Futures Markets, 1989, 8(2), 222-239. [9] Jensen, M.C., Risk, the pricing of capital assets, and the evaluation of investment portfolios. J. Bus., 1969, 42(2), 167-247. doi: 10.1086/295182 [10] Jewitt, I., Risk aversion and the choice between risky prospects: The preservation of comparative statics results. Rev. Econ. Stud., 1987, 54(1), 73-85. doi: 10.2307/2297447 · Zbl 0604.90020 [11] Lorig, M., Indifference prices and implied volatilities. Math. Finance, 2018, 28(1), 372-408. doi: 10.1111/mafi.12129 · Zbl 1403.91347 [12] Lorig, M., Pagliarani, S. and Pascucci, A., Analytical expansions for parabolic equations. SIAM J. Appl. Math., 2015, 75(2), 468-491. doi: 10.1137/130949968 · Zbl 1332.35140 [13] Lorig, M., Pagliarani, S. and Pascucci, A., Explicit implied volatilities for multifactor local-stochastic volatility models. Math. Finance, 2017, 27(3), 926-960. doi: 10.1111/mafi.12105 · Zbl 1422.91713 [14] Merton, R.C., Lifetime portfolio selection under uncertainty: The continuous-time case. Rev. Econ. Stat., 1969, 51, 247-257. doi: 10.2307/1926560 [15] Pagliarani, S. and Pascucci, A., Analytical approximation of the transition density in a local volatility model. Cent. Eur. J. Math., 2012, 10(1), 250-270. doi: 10.2478/s11533-011-0115-y · Zbl 1246.91137 [16] Pham, H., Continuous-time Stochastic Control and Optimization with Financial Applications, Vol. 61, 2009 (Springer Science & Business Media: Berlin). · Zbl 1165.93039 [17] Sharpe, W.F., Mutual fund performance. J. Bus., 1966, 39(1), 119-138. doi: 10.1086/294846 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.