Questions about models for the valuation of option contracts.

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288 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 ...
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1answer
152 views

Selling an American call option early

I understand it is never optimal to exercise an American call option early. [1] [2] However, here are my two contradictory thoughts about selling an American call option early. Assumptions I can ...
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2answers
93 views

Joint distribution from expectations

Given two random variables $X$ and $Y$ and let $K$ be a constant value. Assume the expectation $\mathbb{E}[X(Y-K)^{+}]$ is given for all possible values of $K\geq 0$. Is there a way to derive the ...
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3answers
190 views

Is there any other way to measure option pricing model performance than proximity to market prices?

Short version Why do we take market prices as the prices to be estimated and predicted? The common answer is efficient markets hypothesis as in "Market agents do their best effort given their ...
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1answer
574 views

Implied state price density (Question 1 - derivation of the formula)

I came upon the term "implied state price density" in a couple of papers. As far as I understand the concept one basically tries to extract the "pricing density" from the market data. For the sake ...
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168 views

why is the BNS model the way it is

what I am puzzled about is, why dont we instead of having \begin{equation} dX_t = \sqrt{V_t} dB_t - (\frac{1}{2} V_t^2-r-\lambda\Phi(\rho)) dt - \rho dZ_{\lambda t}\nonumber \end{equation} we just ...
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2answers
233 views

Basket Option weight sensitivity calculation

I am looking to find/estimate the "greeks"/option price sensitivities/derivatives for a basket option situation. In specific the change in price of a put option associated with a change in weight of a ...
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1answer
193 views

binary tree options pricing model with dividend value - How should I discount the option at?

the expected value of the option given the next period up, down values is: $ Pexp = (p Price_{next, up} + (1 - p) Price_{next, down})/R$ where p is defined as $p = \frac{\exp(-r \times \Delta t) - ...
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1answer
163 views

How does Vega of a call/put behave under the Black-Scholes model?

I have two questions. I would prefer a reference if possible. Is the value of vega bounded for $\sigma\in [0,\infty)$? (I assume so, I imagine it goes to 0 as $\sigma$ go to infinity.) Are there any ...
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1answer
423 views

Arbirtage free price process question in Bjork's Arbitrage Theory in Continuous Time

I am currently working through questions in Bjork's Arbitrage Theory in Continuous Time. However, I am unable to solve the following question, 7.2 in the book. A solution would be greatly appreciated. ...
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1answer
184 views

reinsurance pricing equivalent to option pricing

Is it true that pricing a reinsurance contact is equivalent to pricing an option. Basically a reinsurance just cuts off the risk exposure of the insured institution to a threshold say $K$. So if we ...
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2answers
72 views

Vega hedging with implied volatility smile

I have a problem with vega hedging. Consider the management of an exotic derivative, such as Barrier option. Typically we do the following tasks: selecting a pricing model, say, a local volatility ...
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1answer
42 views

Calculate put price with Black-Scholes and one discrete dividend

I try to solve this exercise: a) Calclculate the price of a 3-month European put option on a non-dividend-paying stock with a strike price of 45 when the current stock price is 40, the risk-free ...
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0answers
18 views

Shorting a Synthetic Long [closed]

I have the following information: Call Premium: 0.30 Put Premium: 40.4 Strike: 130 1-Month Risk-Free Rate: 0% Market Price: $85.00 If I use the Synthetic Long ...
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0answers
63 views

Price of an American call option [closed]

I'm working through revision questions at the moment and we are asked to compute the price of an American call option. Suppose that $dS_t = \sigma S_t dW^*_t, S_0 >0$ Let $0<U<T$ be fixed ...
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1answer
50 views

Call option pricing using CCR model - derivation problem

I'm viewing the following derivation of a Call Option price using the CRR model. There is one piece of the derivation which I cannot understand. \begin{align} C_0 &= e^{-rT} \sum_{i=0}^{N} ...
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2answers
103 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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1answer
91 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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0answers
37 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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45 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
30 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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62 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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268 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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70 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
159 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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245 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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145 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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135 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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99 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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56 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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312 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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124 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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525 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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205 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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222 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
133 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
206 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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141 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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4answers
78 views

analytic formula for the value of an American put option

It seems to be a foolish question but I can't take my mind off from , Is it true that there is no analytic formula for the value of an American put option on a non-dividend-paying stock (or a divident ...
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1answer
349 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
51 views

Binomial pricing model: When the Cox-Ross-Rubinstein assumption is not arbitrage-free

I understand that in an arbitrage-free Binomial model, we assume that $S_{t+1} = S_t \cdot u$ in the event of an up-jump and $S_{t+1} = S_t \cdot d$ in the event of a down-jump. We call $u$ and $d$ ...
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1answer
121 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
162 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
112 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
710 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
229 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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59 views

Citable source: Why implied volatility over dollar prices

I am aware of the reasoning of quoting vanilla options as implied volatilities rather than dollar values. However, I would like to have a literature reference where this is explained, to quote / cite ...
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87 views

Analytical soluton to the Black-Scholes equaiton with a modified European Call Option

Please consider the following modified European Call Option where $ 0 < a \leq 1$. When $a = 1$ the modified European call option is reduced to the standard European call option. ...
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66 views

Local volatility parametrization using the spot

Is it possible to estimate the local volatility using the spot price S at time t instead of the strike price K and the expiry date T ? Any help would be appreciated.
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45 views

The State-Price Deflator in a Binomial pricing model

This question comes from a Financial Economics exam and I'm very confused about a state-price deflator which doesn't seem to exist. I've included the whole question for completeness, but my actual ...