Relevant bibliographies by topics / Equivalent martingale measure (EMM)

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Academic literature on the topic 'Equivalent martingale measure (EMM)'

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Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Equivalent martingale measure (EMM)"

1

SENGUPTA, INDRANIL. "GENERALIZED BN–S STOCHASTIC VOLATILITY MODEL FOR OPTION PRICING." International Journal of Theoretical and Applied Finance 19, no. 02 (2016): 1650014. http://dx.doi.org/10.1142/s021902491650014x.

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In this paper, a class of generalized Barndorff-Nielsen and Shephard (BN–S) models is investigated from the viewpoint of derivative asset analysis. Incompleteness of this type of markets is studied in terms of equivalent martingale measures (EMM). Variance process is studied in details for the case of Inverse-Gaussian distribution. Various structure preserving subclasses of EMMs are derived. The model is then effectively used for pricing European style options and fitting implied volatility smiles.
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HERDEGEN, MARTIN, and MARTIN SCHWEIZER. "STRONG BUBBLES AND STRICT LOCAL MARTINGALES." International Journal of Theoretical and Applied Finance 19, no. 04 (2016): 1650022. http://dx.doi.org/10.1142/s0219024916500229.

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In a numéraire-independent framework, we study a financial market with [Formula: see text] assets which are all treated in a symmetric way. We define the fundamental value ∗S of an asset [Formula: see text] as its super-replication price and say that the market has a strong bubble if ∗S and [Formula: see text] deviate from each other. None of these concepts needs any mention of martingales. Our main result then shows that under a weak absence-of-arbitrage assumption (basically NUPBR), a market has a strong bubble if and only if in all numéraire s for which there is an equivalent local martingale measure (ELMM), asset prices are strict local martingales under all possible ELMMs. We show by an example that our bubble concept lies strictly between the existing notions from the literature. We also give an example where asset prices are strict local martingales under one ELMM, but true martingales under another, and we show how our approach can lead naturally to endogenous bubble birth.
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3

HUBALEK, FRIEDRICH, and THOMAS HUDETZ. "CONVERGENCE OF MINIMUM ENTROPY OPTION PRICES FOR WEAKLY CONVERGING INCOMPLETE MARKET MODELS." International Journal of Theoretical and Applied Finance 03, no. 03 (2000): 559–60. http://dx.doi.org/10.1142/s0219024900000577.

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We study weak convergence of a sequence of (approximating) asset price models Sn to a limiting model S: both Sn and S are multi-dimensional asset price processes with some physical probability measures Pn resp. P, and a natural notion of process convergence is the weak convergence of the induced path probability measures, denoted by (Sn|Pn) resp. (S|P), on the abstract topological space of possible asset price trajectories. For the purpose of no-arbitrage pricing of options or more general derivatives on the model assets, there are two different aspects of this convergence: (i) convergence under the given physical probability measures, (Sn|Pn) → (S|P) and (ii) convergence under suitably chosen equivalent martingale measures (EMM) relevant for pricing derivatives, (Sn|Qn) → (S|Q). A simple example is the convergence of a sequence of discrete-time binomial models to the Black–Scholes model (geometric Brownian motion), where the model markets are complete and hence the choice of Qn resp. Q is unique. This example and the general case of complete limit markets (S|P) have been studied in [1]. In contrast we have several choices for Qn resp. Q when all the model markets are incomplete. A natural choice is the minimum entropy EMM [2, 3], defined as the (unique) EMM R minimizing the relative entropy H(R|P) to the physical measure P, among all EMMs. We prove the following: given that the approximating models converge under the physical measures, (Sn|Pn) → (S|P) — with some mild assumptions on P and on the minimum entropy EMMs Rn for Sn resp. R for S — entropy number convergence implies weak convergence of the minimum entropy option price processes: H(Rn|Pn) → H(R|P) implies (Sn|Rn) → (S|R). Several rigorous examples illustrate the result; cf. also [4].
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4

BENTH, FRED ESPEN, and FRANK PROSKE. "UTILITY INDIFFERENCE PRICING OF INTEREST-RATE GUARANTEES." International Journal of Theoretical and Applied Finance 12, no. 01 (2009): 63–82. http://dx.doi.org/10.1142/s0219024909005117.

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We consider the problem of utility indifference pricing of a put option written on a non-tradeable asset, where we can hedge in a correlated asset. The dynamics are assumed to be a two-dimensional geometric Brownian motion, and we suppose that the issuer of the option have exponential risk preferences. We prove that the indifference price dynamics is a martingale with respect to an equivalent martingale measure (EMM) Q after discounting, implying that it is arbitrage-free. Moreover, we provide a representation of the residual risk remaining after using the optimal utility-based trading strategy as the hedge. Our motivation for this study comes from pricing interest-rate guarantees, which are products usually offered by companies managing pension funds. In certain market situations the life company cannot hedge perfectly the guarantee, and needs to resort to sub-optimal replication strategies. We argue that utility indifference pricing is a suitable method for analysing such cases. We provide some numerical examples giving insight into how the prices depend on the correlation between the tradeable and non-tradeable asset, and we demonstrate that negative correlation is advantageous, in the sense that the hedging costs become less than with positive correlation, and that the residual risk has lower volatility. Thus, if the insurance company can hedge in assets negatively correlated with the pension fund, they may offer cheaper prices with lower Value-at-Risk measures on the residual risk.
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5

Wong, Bernard, and C. C. Heyde. "On changes of measure in stochastic volatility models." Journal of Applied Mathematics and Stochastic Analysis 2006 (December 6, 2006): 1–13. http://dx.doi.org/10.1155/jamsa/2006/18130.

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Pricing in mathematical finance often involves taking expected values under different equivalent measures. Fundamentally, one needs to first ensure the existence of ELMM, which in turn requires that the stochastic exponential of the market price of risk process be a true martingale. In general, however, this condition can be hard to validate, especially in stochastic volatility models. This had led many researchers to “assume the condition away,” even though the condition is not innocuous, and nonsensical results can occur if it is in fact not satisfied. We provide an applicable theorem to check the conditions for a general class of Markovian stochastic volatility models. As an example we will also provide a detailed analysis of the Stein and Stein and Heston stochastic volatility models.
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6

Elliott, Robert J., and Dilip B. Madan. "A Discrete Time Equivalent Martingale Measure." Mathematical Finance 8, no. 2 (1998): 127–52. http://dx.doi.org/10.1111/1467-9965.00048.

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7

Siu, Tak Kuen. "Regime-Switching Risk: To Price or Not to Price?" International Journal of Stochastic Analysis 2011 (December 27, 2011): 1–14. http://dx.doi.org/10.1155/2011/843246.

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Should the regime-switching risk be priced? This is perhaps one of the important “normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, Black-Scholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent martingale measures which may be viewed as the largest space of equivalent martingale measures to incorporate both the diffusion risk and the regime-switching risk. Then we show that an optimal equivalent martingale measure over the canonical space selected by minimizing the relative entropy between an equivalent martingale measure and the real-world probability measure does not price the regime-switching risk. The optimal measure also justifies the use of the Esscher transform for option valuation in the regime-switching market.
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8

Hussein, Boushra Y. "Equivalent Locally Martingale Measure for the Deflator Process on Ordered Banach Algebra." Journal of Mathematics 2020 (June 9, 2020): 1–7. http://dx.doi.org/10.1155/2020/5785098.

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This paper aims at determining the measure of Q under necessary and sufficient conditions. The measure is an equivalent measure for identifying the given P such that the process with respect to P is the deflator locally martingale. The martingale and locally martingale measures will coincide for the deflator process discrete time. We define s-viable, s-price system, and no locally free lunch in ordered Banach algebra and identify that the s-price system C,π is s-viable if and only a character functional ψC≤π exists. We further demonstrate that no locally free lunch is a necessary and sufficient condition for the equivalent martingale measure Q to exist for the deflator process and the subcharacter ϕ∈Γ such that φC=π. This paper proves the existence of more than one condition and that all conditions are equivalent.
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9

Zhu, Yonggang. "Equivalent Martingale Measure in Asian Geometric Average Option Pricing." Journal of Mathematical Finance 04, no. 04 (2014): 304–8. http://dx.doi.org/10.4236/jmf.2014.44027.

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10

Kabanov, Yuri. "In discrete time a local martingale is a martingale under an equivalent probability measure." Finance and Stochastics 12, no. 3 (2008): 293–97. http://dx.doi.org/10.1007/s00780-008-0063-y.

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