Questions about models for the valuation of option contracts.

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80 views

Value a structured note with Black-Scholes

Apologies in advance if this seems like a straight forward question but I'm really unsure how to go about it. Say I have the payoff for a structured note benchmarked against an index and I have a ...
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2answers
72 views

Stock Returns Distribution in Heston Model

There is a paper by Dragulescu and Yakovenko (DY) in 2002 proposing a pdf for the stock returns in the Heston model. However, in a paper by Daniel, Bree and Joseph, they actually perform statistical ...
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1answer
44 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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30 views

Use of Black-Scholes Model on Guaranteed Fund Investment

I am stuck with a revision question at home on Black-Scholes pricing model. The question is on a fund manager selling one unit of the fund to a customer for S(0) at time 0 and then guaranteeing at ...
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39 views

How to value a Binary Option using market data?

Is there a way to calculate the price of a binary option (i.e., an option that pays out 1 dollar when the stock price hits $x$ amount) using market call/put option prices, forward prices, etc. for a ...
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26 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 $ ...
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1answer
26 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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58 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 ...
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82 views

Normalized price process $Z(t)=\frac{\Pi(t)}{B(t)}$

If an interest rate model with the following $P$-dynamics for the short rate. $$dr(t)=\mu(t,r(t))dt+\sigma(t,r(t))d\bar{W}(t)$$ Now consider a $T$-claim of the form $\chi = \Phi(r(T))$ with ...
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161 views

Black Scholes - how to calculate delta with a vol skew

I am trying to calculate the delta of an option at different strike prices where the underlying has a pronounced implied volatility skew in order to correctly hedge an options strategy. Researching ...
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68 views

Underlying changes impact on implied volatility

What are some valid techniques that can be used to simulate how changes in the underlying are most likely to impact implied volatility along with the skew of all strikes for options with the same ...
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1answer
137 views

Does a delta hedged short option guarantee profit of extrinsic value at expiration?

If a trader shorts an option and dynamically delta hedges to ensure the delta is equal to 0 if that option expires out of the money does the trader profit that options extrinsic value at the time of ...
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180 views

The option values are different from two r package - foptions,rquantlib

The results are very different.I know the code from quantlib and the result of quantlib seem right(close to market price). Is there anyone know why the value from fOptions is so large or fOptions used ...
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120 views

Pricing binary options with kernel density estimation

Suppose I have a large enough set of prices of an asset, from which I can extract the following function: $f:T\to\mathcal{D}$, where $T$ is a fixed finite set of time intervals (say, 1 minute, 2 ...
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106 views

A question about pricing convertible bond with two different underlying assets

I have a question regarding the pricing of convertible bond. If I value the convertible bond with two different underlying assets, how can I incorporate two volatility and the correlation in the ...
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74 views

American Swaption Pricing with PDE discretization

So I am still trying to price an american swaption. (MC approach here: American Swaption Pricing with Monte-Carlo method) I've found in Paul Wilmott, The mathematics of financial derivatives, a PDE ...
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51 views

Incorporating a stochastic correlation structure into a multi-factor model

I am considering extending a multi-factor fixed income stochastic model (e.g. LIBOR-Market) to use stochastic correlation matrices instead of determinstic ones. For pricing instruments with short ...
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289 views

Pricing options and bid-ask spread

Consider a non-liquid option market with a wide bid-ask spreads across all strikes. Spot: \$52 A snapshot of the \$50 strike shows: ...
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119 views

Do you use software for finite element valuation or do you roll your own?

Engineers put a lot of time and effort in developping high quality finite element (FE) software (deal.II, Dune, Elmer,...). So I was wondering if some of those tools would be suitable for quantitative ...
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416 views

Implied volatility and greeks for american option with discrete dividends

What methods are available to calculate IV and greeks for an american option with discrete dividends, and how do they compare? Should I use Roll-Geske-Whaley and solve for a given option price?
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180 views

How to statistically compare the pricing errors of various option pricing models?

I have three different option pricing models, for which I computed the in-sample and out-of-sample pricing errors. Now I want to test the pricing performance of these three option pricing models ...
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189 views

Pricing a Power Contract derivative security

I'm trying to price a "power contract" and would appreciate guidance on the next step. The payoff at time $T$ is $(S(T)/K)^\alpha$, where $K > 0$, $\alpha \in \mathbb{N}$, $T > 0$. $S$ is ...
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1answer
130 views

Am I reading this correctly? probability way too small with BS model

For a stock trading at $27, $28 strike, 0% interest, 15% annual vol, and one day until expiration there is about a 1 in 17000 chance of it being exercised? $d_2 = ...
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1answer
200 views

Exotic option pricing

I'm trying to price an option with payoff $\max\{a\cdot S_t - K,0\}$ where $a$ is a known constant. Ideally I'm looking for a closed form, continuous-time solution. Where should I begin?
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2answers
102 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 ...
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1answer
318 views

Does an option's price “ratio” with the underlying security price?

I'm trying to understand option pricing better. Let's say security ABC is \$40, and a 38 PUT option with 40% implied volatility (and 90 days till expiration) is priced at X. If security ABC then ...
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1answer
106 views

Black-box local volatility pricer

I am testing a local volatility pricer by comparing its results under two settings: Pricing a 5yr ATM call option with a flat volatility of $0.194$ Pricing the call option with the typically shaped ...
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3answers
140 views

Divergence between binomial pricing and monte carlo simulation for vanilla european call?

I notice a divergence in my own code, but it's evident even in public code: http://www.thalesians.com/finance/index.php/Knowledge_Base/Finance/Option_Pricing_in_Python_and_Simple_English Pricing a ...
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1answer
109 views

Reference on SDE driven by jump processes

Are there reference on SDE driven by jump proccesses? e.g. Shepard-Nielson Model
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1answer
627 views

Which prediction market model is efficient and simple to use?

For a college project I'm tasked with implementing prediction market. Which model of it I'd better choose? I want something useful and simple enough for other people to quickly understand and use. ...
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1answer
223 views

What are the rules for quoting option prices on the market?

I have implemented a monte carlo pricer for an option. I simply don't know how many decimals I need to include in the quoted price. Can anyone please provide guidelines?
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1answer
48 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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1answer
615 views

Asset-or-nothing Option Valuation in the Black and Scholes model

In standard Black-Scholes Model, compute the price of an asset-or-nothing put and asset-or-nothing call options. Write down the put-call parity relation between the asset-or-nothing call and put ...
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1answer
45 views

binomial option pricing model - problem with risk-neutral probability

I have a little problem: in the binomial option pricing model, the price of a european derivative security $V_{n}$ satisfies: $V_{n}=[1/(1+r)]*[\tilde{p}*optionUp +\tilde{q}*optionDown]$ where: ...
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2answers
112 views

Pricing of Binary or Digital Options or more generally options with discontinuous payoffs using PDEs

I am trying to find references (books, papers, etc.) for calculating $\mathbb E f(X_T)$, where $X_T$ is a diffusion and $f$ is a real function that is not continuous, by means of solving a PDE or ...
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1answer
56 views

Why theta multipled by days to expiry exceeds the total time premium of the option

Sometimes, I find an option where the total time value of the option may be 5 cents(rest is intrinsic value) and there are about 15 days to expiry and theta is .08 (8 cents). How is this possible. If ...
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1answer
29 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
58 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 ...
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3answers
154 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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1answer
129 views

Intuitive understanding of Black-Scholes pricing

The Black-Scholes formula entails market completeness, so the price of an option is only the cost associated with dynamically hedging the option. Where does this cost come from? I don't see how ...
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1answer
68 views

Sample size and historical correlation matrices

I was wondering whether any literatures existed on how to properly estimate correlation matrices from historical data. Obviously the entire procedures allows a lot of leeway. The frequency of ...
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4answers
665 views

compute sharpe ratio for options?

Calculating sharpe ratio for shares is a straight forward task: (average returns - risk free ) / standard deviation. However i remain baffled as to how to tackle the task for options, can someone ...
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1answer
114 views

Symmetry of option-implied probability density

I was wondering whether the option implied probability density of the log returns: $x = \ln\left(\frac{S}{S_0}\right)$ with S the value of a certain stock, is always symmetric ? I was asking myself ...
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170 views

Numerical difficulties in fitting option prices

In [1], the authors state that "Although some studies apply the curve-fitting method directly to option prices, the severely nonlinear relationship between option price and strike price often leads to ...
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1answer
369 views

Question on OptionMetrics: “Strike Price times 1000” differs too much from Index price

I have a question regarding the strike price that is given on OptionMetrics. My goal is to primarily retrieve options prices of a specific maturity with strike prices that are 20% in-the-money, ...
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1answer
14 views

What does “convergence” in Monte Carlo simulation mean?

I have read about convergence in terms of MC simulation for derivative pricing, but I am not clear on what it exactly means. Let us suppose I price an option 100,000 paths twice and both result in the ...
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44 views

Put-Call relationship for Option on Forward

How do i show that the prices of European call, C, and put options, P, on the forward F, with the same strike K and expiry date $T_1$, where $T_1 < T$ (ie, the options expire before the forward ...
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Will a back month leg in call calendar lose value if underlying goes down

If I buy a call calendar and underlying drops 5%, the front month short call will get further out of money and will lose value, resulting in a gain since I am short the front month option. What about ...
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Exercise 2.2 from the book “The concept and practice of Mathematical Finance”

I am a newbie. Please help me understand how to resolve the exercise 2.2 from the book "The concept and practice of Mathematical Finance". The solution from the book says that our super-replicating ...
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Why does the OTM call sometimes have a higher theta than the ATM call?

In this AAPL option chain on Mar20 call options, the OTM calls have a slightly higher theta than the ATM calls. Why is this? Is not time value(and thereby time decay) supposed to be highest for ...