Pricing average options on commodities

Shiraya, Kenichiro; Takahashi, Akihiko

doi:10.1002/fut.20481

Cited by 36 publications

(20 citation statements)

References 17 publications

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“…Yamazaki (2012) proposed an analytical approximation formula for pricing arithmetic Asian options based on the Gram-Charlier expansion. Takahashi (2011), Shiraya, Takahashi, andYamada (2012) and Shiraya, Takahashi, and Toda (2012) provided approximation methods for pricing discrete barrier and arithmetic Asian options by an asymptotic expansion based on the Malliavin calculus. Fang and Oosterlee (2011) applied the Fourier cosine expansion and high-order quadrature rules to evaluate discrete barrier options.…”

Section: Review Of the Related Literaturementioning

confidence: 99%

Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Lévy Processes

Umezawa

Yamazaki

2014

Applied Mathematical Finance

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This paper proposes a pricing method for path-dependent derivatives with discrete monitoring when an underlying asset price is driven by a time-changed Lévy process. The key to our method is to derive a backward recurrence relation for computing the multivariate characteristic function of the intertemporal joint distribution of the time-changed Lévy process. Using the derived representation of the characteristic function, we obtain semi-analytical pricing formulas for geometric Asian, forward start, barrier, fader and lookback options, all of which are discretely monitored.

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Section: Review Of the Related Literaturementioning

confidence: 99%

Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Lévy Processes

Umezawa

Yamazaki

2014

Applied Mathematical Finance

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“…This study extends Shiraya and Takahashi (2011) to the cross-currency correspondents, which is very useful for firms outside U.S. importing energies such as crude oils traded mainly with the U.S. dollar (USD). Especially, we evaluate average options on Japanese yen (JPY) based West Texas Intermediate (WTI) futures, where SABR model is applied to WTI futures price processes whereas an extended l-SABR model is used for the JPYUSD spot foreign exchange rate 1 process.…”

Section: Introductionmentioning

confidence: 95%

“…In this case, setting the weights as

w_{1} (t) = 1

w_{2} (t) = - 1

and

w_{i} (t) = 0

(i = 2, \dots, n)

, we have

X (t) = Y_{1} (t) - Y_{2} (t) .

Basket optionsThe underlying asset of a basket option is the weighted average of the prices of different assets, where the weights are typically some prespecified (positive) constants, that is

w_{i} (t) \equiv w_{i} > 0

for all i :

X (t) = \sum_{i = 1}^{n} w_{i} Y_{i} (t) .

Average optionsAverage options are one of popular products especially in the commodity markets; the futures contracts with several consecutive maturities may become the underlying assets of an average option as in over the counter oil market (e.g., WTI market). (See Shiraya & Takahashi, , for the detail of the structure of products. )More generally, let us introduce new processes

Z_{i} (t)

defined by

Z_{i} (t) = \sum_{j = 1}^{m_{i}} Y_{i} (t_{j}^{(i)}) I (({} t_{j}^{(i)} \leq t)),

where

0 \leq t_{1}^{(i)} < \dots < t_{m_{i}}^{(i)} \leq T

m_{i}

denotes the number of the cross‐currency price

Y_{i ...}

…”

Section: Multiasset Cross‐currency Optionsmentioning

confidence: 99%

“…For the WTI futures price processes

S_{i}

(

i = 1, 2

), We take SABR model with

β = 0.5, 1

, because our previous analysis in Shiraya and Takahashi () has found that SABR model can achieve good calibration to the WTI futures option market. (See Shiraya & Takahashi, for the detail. )…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Average options are one of popular products especially in the commodity markets; the futures contracts with several consecutive maturities may become the underlying assets of an average option as in over the counter oil market (e.g., WTI market). (See Shiraya & Takahashi, 2011, for the detail of the structure of products.) More generally, let us introduce new processes Z i ðtÞ defined by…”

Section: Average Optionsmentioning

confidence: 99%

See 2 more Smart Citations

Pricing Multiasset Cross‐Currency Options

Shiraya

Takahashi

2012

Journal of Futures Markets

Self Cite

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This study develops a general pricing method for multiasset cross‐currency options, whose underlying asset consists of multiple different assets, and the evaluation currency is different from the ones used in the most liquid market of each asset; the examples include cross‐currency options, cross‐currency basket options, and cross‐currency average options. Moreover, in practice, fast calibration is necessary in the option markets relevant for the underlying assets and the currency, which is also achieved in this study. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:1–19, 2014

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Recursive Formula for Arithmetic Asian Option Prices

Lee

2012

Journal of Futures Markets

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We derive a recursive formula for arithmetic Asian option prices with finite observation times in semimartingale models. The method is based on the relationship between the riskneutral expectation of the quadratic variation of the return process and European option prices. The computation of arithmetic Asian option prices is straightforward whenever European option prices are available. Applications with numerical results under the BlackScholes framework and the exponential Lévy model are proposed.

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Pricing average options on commodities

Cited by 36 publications

References 17 publications

Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Lévy Processes

Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Lévy Processes

Pricing Multiasset Cross‐Currency Options

Recursive Formula for Arithmetic Asian Option Prices

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