If indices fall by 10 percent, shorts will rise by the same amount, right? Buckle up, we�re in fo... more If indices fall by 10 percent, shorts will rise by the same amount, right? Buckle up, we�re in for a ride
Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. www.econstor.eu C Ce en nt tr re e f fo or r P Pr ra ac ct ti ic ca al l Q Qu ua an nt ti it ta at ti iv ve e F Fi in na an nc ce e
Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. www.econstor.eu C Ce en nt tr re e f fo or r P Pr ra ac ct ti ic ca al l Q Qu ua an nt ti it ta at ti iv ve e F Fi in na an nc ce e
Options with discontinuous payoffs are generally traded above their theoretical Black-Scholes pri... more Options with discontinuous payoffs are generally traded above their theoretical Black-Scholes prices because of the hedging difficulties created by their large delta and gamma values. A theoretical method for pricing these options is to constrain the hedging portfolio and incorporate this constraint into the pricing by computing the smallest initial capital which permits superreplication of the option. We develop this idea for exotic options, in which case the pricing problem becomes one of stochastic control. Our motivating example is a call which knocks out in the money, and explicit formulas for this and other instruments are provided.
With continuous time in a local vol model one needs to apply extra care when using the probabilit... more With continuous time in a local vol model one needs to apply extra care when using the probability density second order derivative further in the Dupire formula along with the time-derivative to compute local volatilities
KOAMKIEU refers to a double barrier option, with an American knock-out (KOAM) barrier and a Europ... more KOAMKIEU refers to a double barrier option, with an American knock-out (KOAM) barrier and a European knock-in barrier (KIEU)
Highlighting a few shortcuts in option pricing, in the spirit of sanity checks, quick answers, an... more Highlighting a few shortcuts in option pricing, in the spirit of sanity checks, quick answers, and passing interview questions.
I n my options training courses, I often ask participants if a long vanilla option can be both lo... more I n my options training courses, I often ask participants if a long vanilla option can be both long gamma and long theta. Normally, options textbooks train us that the value of an option is the sum of its intrinsic value and the time value. As time progresses, the value converges to the payoff function, and the time value converges to zero. It is one of the common misconceptions 1 that time value is always positive. If the forward curve goes down (backwardation), the time value can be negative for in-the-money options, i.e., the value of the call option is less than the payoff function. And in FX markets, this is quite common. As an example, we consider a market in USD-JPY, where USD interest rates are higher than JPY interest rates, and therefore the forward curve decreases. With a negative time value, we would then conclude that a deep in-the-money long USD call JPY put option is long gamma (because the payoff is convex) and long theta, because the value is below the payoff and converges up to the payoff. Today, we stretch this phenomenon a bit further and show that such a USD call can be short theta after all and will further learn that it can be both short theta and long theta. No kidding. The market I consider is USD-JPY spot 127.00 on the trade day May 26, 2022, with spot date May 3, USD six-month money market interest rate 1.77%, JPY six-month money market interest rate-0.40% (yielding a six-month forward rate of 125.61 below initial spot), ATM volatility 9.634%, 25-delta risk reversal-0.654% (favoring USD puts), 25-delta butterfly 0.441% (standard). All at the same time. No kidding.
Can a Butterfly be negative, and why do we use the probability density to check for Butterfly arb... more Can a Butterfly be negative, and why do we use the probability density to check for Butterfly arbitrage?
Isn't there anything cheaper than vanilla options? From an actuarial point of view a put or a... more Isn't there anything cheaper than vanilla options? From an actuarial point of view a put or a call option is an insurance against falling or rising exchange rates, and surely a buyer would like to keep the premium at a minimal level. For this reason barrier options have been invented. They belong to the first generation exotics. The premium can be lowered by shifting risk to the option holder. We give an overview of the issues related to barrier options
If indices fall by 10 percent, shorts will rise by the same amount, right? Buckle up, we�re in fo... more If indices fall by 10 percent, shorts will rise by the same amount, right? Buckle up, we�re in for a ride
Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. www.econstor.eu C Ce en nt tr re e f fo or r P Pr ra ac ct ti ic ca al l Q Qu ua an nt ti it ta at ti iv ve e F Fi in na an nc ce e
Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. www.econstor.eu C Ce en nt tr re e f fo or r P Pr ra ac ct ti ic ca al l Q Qu ua an nt ti it ta at ti iv ve e F Fi in na an nc ce e
Options with discontinuous payoffs are generally traded above their theoretical Black-Scholes pri... more Options with discontinuous payoffs are generally traded above their theoretical Black-Scholes prices because of the hedging difficulties created by their large delta and gamma values. A theoretical method for pricing these options is to constrain the hedging portfolio and incorporate this constraint into the pricing by computing the smallest initial capital which permits superreplication of the option. We develop this idea for exotic options, in which case the pricing problem becomes one of stochastic control. Our motivating example is a call which knocks out in the money, and explicit formulas for this and other instruments are provided.
With continuous time in a local vol model one needs to apply extra care when using the probabilit... more With continuous time in a local vol model one needs to apply extra care when using the probability density second order derivative further in the Dupire formula along with the time-derivative to compute local volatilities
KOAMKIEU refers to a double barrier option, with an American knock-out (KOAM) barrier and a Europ... more KOAMKIEU refers to a double barrier option, with an American knock-out (KOAM) barrier and a European knock-in barrier (KIEU)
Highlighting a few shortcuts in option pricing, in the spirit of sanity checks, quick answers, an... more Highlighting a few shortcuts in option pricing, in the spirit of sanity checks, quick answers, and passing interview questions.
I n my options training courses, I often ask participants if a long vanilla option can be both lo... more I n my options training courses, I often ask participants if a long vanilla option can be both long gamma and long theta. Normally, options textbooks train us that the value of an option is the sum of its intrinsic value and the time value. As time progresses, the value converges to the payoff function, and the time value converges to zero. It is one of the common misconceptions 1 that time value is always positive. If the forward curve goes down (backwardation), the time value can be negative for in-the-money options, i.e., the value of the call option is less than the payoff function. And in FX markets, this is quite common. As an example, we consider a market in USD-JPY, where USD interest rates are higher than JPY interest rates, and therefore the forward curve decreases. With a negative time value, we would then conclude that a deep in-the-money long USD call JPY put option is long gamma (because the payoff is convex) and long theta, because the value is below the payoff and converges up to the payoff. Today, we stretch this phenomenon a bit further and show that such a USD call can be short theta after all and will further learn that it can be both short theta and long theta. No kidding. The market I consider is USD-JPY spot 127.00 on the trade day May 26, 2022, with spot date May 3, USD six-month money market interest rate 1.77%, JPY six-month money market interest rate-0.40% (yielding a six-month forward rate of 125.61 below initial spot), ATM volatility 9.634%, 25-delta risk reversal-0.654% (favoring USD puts), 25-delta butterfly 0.441% (standard). All at the same time. No kidding.
Can a Butterfly be negative, and why do we use the probability density to check for Butterfly arb... more Can a Butterfly be negative, and why do we use the probability density to check for Butterfly arbitrage?
Isn't there anything cheaper than vanilla options? From an actuarial point of view a put or a... more Isn't there anything cheaper than vanilla options? From an actuarial point of view a put or a call option is an insurance against falling or rising exchange rates, and surely a buyer would like to keep the premium at a minimal level. For this reason barrier options have been invented. They belong to the first generation exotics. The premium can be lowered by shifting risk to the option holder. We give an overview of the issues related to barrier options
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Papers by Uwe Wystup