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Option-pricing in incomplete markets: the hedging portfolio plus a risk premium-based recursive approach

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dc.affiliation.dptoUC3M. Departamento de Economía de la Empresaes
dc.contributor.authorIbáñez, Alfredoes
dc.date.accessioned2006-11-29T11:07:42Z
dc.date.available2006-11-29T11:07:42Z
dc.date.issued2005-01es
dc.description.abstractConsider a non-spanned security $C_{T}$ in an incomplete market. We study the risk/return tradeoffs generated if this security is sold for an arbitrage-free price $\hat{C_{0}}$ and then hedged. We consider recursive "one-period optimal" self-financing hedging strategies, a simple but tractable criterion. For continuous trading, diffusion processes, the one-period minimum variance portfolio is optimal. Let $C_{0}(0)$ be its price. Self-financing implies that the residual risk is equal to the sum of the one-period orthogonal hedging errors, $\sum_{t\leq T} Y_{t}(0) e^{r(T -t)}$. To compensate the residual risk, a risk premium $y_{t}\Delta t$ is associated with every $Y_{t}$. Now let $C_{0}(y)$ be the price of the hedging portfolio, and $\sum_{t\leq T}(Y_{t}(y)+y_{t}\Delta t)e^{r(T-t)}$ is the total residual risk. Although not the same, the one-period hedging errors $Y_{t}(0) and Y_{t}(y)$ are orthogonal to the trading assets, and are perfectly correlated. This implies that the spanned option payoff does not depend on y. Let $\hat{C_{0}}-C_{0}(y)$. A main result follows. Any arbitrage-free price, $\hat{C_{0}}$, is just the price of a hedging portfolio (such as in a complete market), $C_{0}(0)$, plus a premium, $\hat{C_{0}}-C_{0}(0)$. That is, $C_{0}(0)$ is the price of the option's payoff which can be spanned, and $\hat{C_{0}}-C_{0}(0)$ is the premium associated with the option's payoff which cannot be spanned (and yields a contingent risk premium of sum $y_{t}\Delta$t$ e^{r(T-t)}$ at maturity). We study other applications of option-pricing theory as well.es
dc.format.extent885966 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.repecwb058121
dc.identifier.urihttps://hdl.handle.net/10016/488
dc.language.isoenges
dc.relation.ispartofseriesUC3M Working Papers. Bussiness Economicses
dc.relation.ispartofseries2005-21es
dc.rights.accessRightsopen access
dc.subject.ecienciaEmpresa
dc.titleOption-pricing in incomplete markets: the hedging portfolio plus a risk premium-based recursive approaches
dc.typeworking paper*
dspace.entity.typePublication
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