Questions about models for the valuation of option contracts.

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51 views

Does a call calendar lose its entire value if underlying increases well past the strike?

If I buy a call calendar spread, and the underlying increases, both options are in the money by the expiry of the short call. So both options increase in value, but the short one increases less ...
4
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2answers
242 views

Does higher vega imply higher IV and vice versa

If an option A has higher vega than option B, does that also mean that A has a higher IV than B? I understand that by definition, a higher vega means that A's price is more sensitive to its IV than B. ...
2
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1answer
86 views

If an option went down in value, how much is due to theta decay and how much due to fall in IV

Let us say that there was a stock trading at 100 and the 105 call was trading at 3 $. with 1 month to go Now stock went up to 104 after 15 days, and the call dropped to 2.80 $, to the call buyer's ...
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1answer
53 views

Pricing of a call option in one period binomial model

You are given a $5\%$ call option worth $\$2.66$. The strike price $k$ is $\$41.00$. $S(0)=40$, $Sd=35$ (i.e the lower price of the stock at $t=1$) find $Su$ (i.e the high price of the stock at ...
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1answer
173 views

Why implied volatility is less for the back month option even though the back month option is more expensive

Why is the implied volatility of this option at the ATM strike (18$) greater in the front month (March) than in a further month (Oct). The Oct month has 43%, but the front month has 54%. Should not ...
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2answers
127 views

Black Scholes: How does it help to transform uncertainty and still not be able to calculate a fair price?

Recapitulating the history of Black-Scholes: Nobody knows the fair price of options. Revolution: BS! You put in all the parameters and get a price -> A Nobel Prize for that one! Wait: Nobody knows ...
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4answers
8k views

How should I calculate the implied volatility of an American option in a real-time production environment?

There are many models available for calculating the implied volatility of an American option. The most popular method, employed by OptionMetrics and others, is probably the Cox-Ross-Rubinstein model. ...
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2answers
168 views

How to price an European call on zero-coupon from the yield curve?

It is known that the price of an European call of maturity $T^*$ on zero-coupon of maturity $T$ is given by $$p(0,T)= B(0,T^*)\mathbb E ^{\mathbb Q_{T^*}}\left[ (B(T^*,T)-K)^+\right]$$ where ...
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0answers
66 views

How to apply the chain rule for partial derivatives to transformations?

I'm currently working to solve the Black-Scholes model partial differential equation (it's a model for a.o. stock option prices). The Black-Scholes equation for a calloption C(S,t) is given by $ ...
2
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1answer
121 views

option pricing with limitation on the change of underlying daily changes

how are we supposed to price an European option given the fact that the daily return of the underlying is limited within -X% to X%? For example, if X = 5, the price of the underlying cannot go up 8% ...
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1answer
31 views

Spread options on prices or returns?

I need some clarifications regarding spread options. I have always found them characterized as paying, at maturity, the difference between the prices of two underlying assets: $$ (S_1(T)-S_2(T)-K)^+ ...
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2answers
389 views

Pricing an american style option on a bond future

what is the good way to pricing american option on bond future? From bonk fixed income securities 3rd by Tuckman, I understand how to pricing European option on bond future, but I still have no clue ...
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2answers
5k views

What causes the call and put volatility surface to differ?

I currently have a local volatility model that uses the standard Black Scholes assumptions. When calculating the volatility surface, what causes the difference between the call volatility surface, ...
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1answer
66 views

Magrabe Exchange Option: not equal drifts

I need to calculate the price of exchange option between 2 assets $S_1$ and $S_2$ The formula is given here Wiki: Magrabe formula or here Quant Stack Exchange. In the derivation of the formula it is ...
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2answers
86 views

Option greeks: sensitivity to 1% move

In a Black&Scholes framework how can I compute the following sensitivities: to 1% move in the underlying price to 1% move in implied volatility I would like the greeks to tell me how many ...
2
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2answers
225 views

Is it fair to assume $(ud=1)$ in the binomial tree option pricing model?

I have discussion with my colleague on why a general assumption $$ud=1$$ in binomial tree option pricing model would be necessary? I take it a simplification of the problem, otherwise, there will be ...
3
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1answer
185 views

Data Selection for Empirical Pricing Kernel Estimation (Stochastic Discount Factor)

I want to estimate an empirical pricing kernel for an index. Hence, I need to estimate a physical and risk neutral density. For estimating the physical density, only the index data in an observed time ...
2
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1answer
236 views

Some questions about implied volatilities and how to generate theoretical prices when market prices are not available

I am building a little Excel file that take some option prices in input and plots the volatility smile/surface. I have a script that reads market prices from the option chain for 3 different ...
2
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1answer
93 views

Price an option whose strike price is always lower than the future price of the security

Suppose it is known that the price of a certain security after one period will be one of the $m$ values $s_1,\ldots,s_m$. What should be the cost of an option to purchase the security at time $1$ for ...
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0answers
72 views

Value of an option to exchange an asset for another

I'm working out the examples in the paper "Changes of Numeraire, Changes of Probability Measure and Option Pricing", corollary 3. An option of exchanging asset 2 against asset 1 at time T, its time-0 ...
2
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3answers
158 views

Replication of a call option by cash-or-nothing digital option

I am so stuck on this question: Consider a two-asset model where asset 0 is cash, so that the price of asset 0 is $B_t=1$ for all $t \geq0$. Asset 1 has prices given by $dS_t = a(S_t) dW_t$, where the ...
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1answer
140 views

Asymptotic behavior of theta of vanilla call option

It is well known that the theta of call option is always negative. Also, the theta of (at the money call option) goes to infinity as the time approaches to the maturity. On the other hands, (ITM and ...
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1answer
139 views

How to price a futures spread option?

Let's say I have two futures contract $F_1(0,T)$ and $F_2(0,T)$ on two different correlated underlyings. If I assume that both underlying follow a GBM with volatility $\sigma_1$ and $\sigma_2$ ...
2
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3answers
163 views

Pricing exotic option whose payout depends on the stopping time

I am struggling with this question: Let $B$ be a standard Brownian motion. In a Black-Scholes model, at time $t$, the stock price is given by \begin{equation} S_t = \exp \{ \sigma B_t + ( r- ...
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3answers
543 views

forward implied volatility skew

I would like to calculate implied forward volatility skew. I have stochastic volatility monte carlo. What kind of payoff do I need to price and how to use Black() formula to calculate the implied ...
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2answers
565 views

Price of a composite option

how would you calculate the fair value of an option on a fx'ed underlying, e.g. a put on a USD-stock which is changed into EUR? How should I get, in practice, the fx spot vol/correl? Purpose is to ...
4
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1answer
199 views

Analysis of Unbalanced Covered Calls

Hello I am doing an analysis on covered calls with and extra amount of naked calls. Ignore the symbol and current macroeconomic events. I couldn't find any reference to this strategy (unbalanced is ...
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2answers
239 views

Dupire model and Local Volatility model

In the context of Option pricing model. Is there a difference between the Dupire Model and the Local volatility model ? Thanks Achal
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1answer
153 views

Implication of the Greeks under jump diffusion model

Consider jump diffusion model proposed by Merton and Kou. As far as i know, most paper only dealt the valuation of option under the jump diffusion model. As i expected, because of the ...
0
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2answers
261 views

Why gamma for ATM option decreases as volatility increases

Why is the gamma for an at the money option less when volatility increases. Intuitively ,I thought that increasing volatility means more uncertainty,hence the option price will be more sensitive to ...
6
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1answer
909 views

What are the main flaws behind Ross Recovery Theorem?

Stephen Ross’ new paper claims that it is possible to separate risk aversions and historical probabilities if the Stochastic Discount Factor is transition independent using Perron-Frobenius Theorem. ...
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4answers
940 views

Software for decomposing structured products into plain vanilla products

Nowadays structured products (or packages) with complex payoff diagrams are omnipresent. Do you know of any software, add-ons, apps, code whatever, that enables you to enter a payoff diagram or a ...
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1answer
59 views

Pricing rule shall be a martingale measure

In the book "Financial Modelling with jump processes" by Cont and Tankov there is a chapter that explains martingale pricing principles. It is not extremely formal, but gives the idea underlying the ...
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5answers
3k views

How to get greeks using Monte-Carlo for arbitrary option?

Let's assume I have an arbitrary option that I can price using Monte-Carlo simulation. What is the general approach (i.e. without relying on specific option type) to calculating the greeks in this ...
4
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1answer
281 views

Practical implementation of Least Squares Monte Carlo (tweaks and pittfalls)

The Longstaff-Schwartz LSM approach is nowadays ubiquitous(at least in the academic literature) in pricing path dependant derivatives. Up to now I have mostly worked with lattice methods. My ...
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1answer
560 views

What is the difference between market efficiency, market equilibrium, and no-arbitrage?

Aaron Brown (in the book, The Poker Face of Wall Street, p. 196), discusses four approaches to deriving the same Black-Scholes-Merton option-pricing formula: Ed Thorp, Myron Scholes, Robert ...
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1answer
172 views

What is the stochastic differential of a general semimartingale?

By using the canonical representation of a semimartingale in Eberlein, Glau and Papapantoleon's "Analysis of Fourier Transform Valuation Formulas and Applications", on page 3: $$H = B + H^c + h(x) ...
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1answer
189 views

Implied volatility and pricing of vanilla options

As far as I understood, implied volatility (IV) is a lucky parametrization of the vanilla option's price. That is, instead of deciding how much the call worth now, you can decide on its IV and put ...
4
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1answer
592 views

SABR calibration: simple explanation and implementation

I would like to learn more about the SABR model and ho it is used in modeling smiles in equity, FX and rates markets. How would you explain the process and its implementation in simple steps? Any web ...
0
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1answer
51 views

how to use known premium of options to determine premium of options with another strike?

Assuming constant volatility across all strikes, how to use known premium of options to determine premium of options with another strike? e.g. suppose we know premium of \$40 call and put, \$50 call ...
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0answers
147 views

negative transition probabilities in the heston model

I've been trying to implement a bivariate tree for pricing american options with the heston model in R using the paper of Beliaeva and Nawalkha ...
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1answer
88 views

Pricing American with floating strike

Consider a American floating strike put option with maturity $T$, written on a non-dividend paying stock $S_t$. The strike of this option at time $t\leq T$ is $Ke^{-r (T-t )}$, where $r$ is the ...
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1answer
665 views

Solving Black-Scholes PDE using Laplace transform

I'm trying to obtain the Laplace transform of Call option price with repect to time to maturity under the CEV process. The well known Black scholes PDE is given by $$ ...
4
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1answer
164 views

Literature on Empirical Option Pricing

When I started combing through the literature I was astonished about how little the option pricing models are tested against market data and benchmarks are limited. The main barrier is of course ...
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2answers
274 views

Valuation of barrier options in Jump diffusion model

I am trying to evaluate the value of a Barrier option using Monte carlo method. The stock follows a jump diffusion model. I am using the method described in Metwally and Atiya. The authors describe ...
2
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1answer
290 views

Closed form european option prices for a variance gamma process with a randomly distributed drift, volatility, and variance rate

Does an option pricing model with a closed form European option price exist that takes into account randomly distributed drift, volatility, and variance rate? I prefer a modification to the variance ...
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3answers
434 views

Option on a dice game

I am sligtly confused by this problem, although it should not be difficult. Let us roll a sigle dice. If the dice shows $n$, I receive $n$ dollars. I can buy an option to roll the die again. What is ...
4
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2answers
399 views

Black-Scholes fastest computation method

What is the fastest way to numerically compute Black-Scholes-Merton option prices? I'm trying to find fastest and still precise method. Currently I'm using numerical approximation of Normal cdf with ...
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3answers
443 views

What is the effect of dividend yield being greater than the risk-free rate to American options pricing?

Even though dividends are discrete, literature often makes the assumption of continuous dividends (mostly in the case of indices but the individual stocks as well). The dividend yield denoted by q is ...
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5answers
1k views

Consensus on Cauchy distribution for stock prices

What is the general consensus for using a Cauchy distribution to model stock prices? I can't find much after researching online and wonder if it has been tried and discarded. My motivation is to find ...