Questions about models for the valuation of option contracts.

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2answers
129 views

Difference between Closing Price, Last traded price and Settlement Price for option contracts?

What is the difference between Closing price, Last traded price and settlement price ? I got the difference between Closing Price and Settlement price from previous post : The difference between ...
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1answer
382 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
59 views

Can a large OpenInt of calls cause a stock to go down?

I read forum post from another site. Which stated... ...
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1answer
78 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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3answers
174 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
113 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
233 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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2answers
74 views

Price of an equity

An equity has a value of 100 Euros, and pay a dividend of 5 Euros in 6 months. The interest rate of 6 months is 5% and the interest rate for 1 year is 6%. I would like to compute the value of the ...
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2answers
105 views

Discrepancy between binomial model, Black-Scholes and Monte-Carlo Simulation

I try to use Monte-Carlo Simulation to price a 10-year call option. Based on below parameter, S = 1, X = 1, volatility = 80%, T = 10, risk-free rate = 0.22% The option value based on Monte-Carlo ...
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1answer
70 views

Does presence of arbitrage necessarily make all derivatives have zero value?

Spin-off from: Pricing when arbitrage is possible through Negative Probabilities or something else I mean in a theoretical sense: If we have a particular market model with some fancy assumptions such ...
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1answer
86 views

Can someone explain to me what's snell envelope?

What is snell intuitively? And what is its use in quantitative finance? Please explain to me as intuitive as possible! As I explained in the comments, I am new to this field and I was hoping someone ...
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1answer
64 views

Binary Option valuation problem in R using RQuantLib; also result validation aspect

When I am trying to value Binary Option using RQuantLib I am not getting all the greeks for exctype "american" wheras "european" exctype is fine. What is the problem here ? ...
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1answer
71 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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1answer
78 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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1answer
80 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 ...
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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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1answer
1k 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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4answers
914 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
33 views

Pricing a vanilla call option with a fixed dividend

I have started a finance course few months ago and am looking for a way to compute the price of a 1-year call option with a fixed dividend paid after 6 months. Using Black and Scholes I know how to ...
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1answer
55 views

completeness of the binomial model - proof

I am reviewing the steps of proof that the binomial model is complete and don't understand the marked in red transition. Could anybody explain this step? If $P^{**}$ is a risk-neutral measure, so ...
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1answer
36 views

Swaption on a swap with 0 year tenor

Any ideas on valuation of IRS swaption on a swap with 0 year tenor? As an example, we have a 5 year swaption, on expiration it is cash settled; the underlying swap tenor is 0 years with excercise and ...
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1answer
59 views

Finding circumstances for price of call = price of put

Here is a problem in Hull's book and the given solution: My approach was to compute the profit $\pi = \pi_{SP} + \pi_{LC}$ (short put, long call). One can show that $\pi = \pi_{SP} + \pi_{LC} = ...
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1answer
83 views

Bond price in Ho-Lee Model

I know Ho-Lee model and want to extract the price at $t$, of a European call option with strike price $K$ and exercise date $T$, on an underlying $S$-bond, but I don't know what way should I choose: ...
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1answer
96 views

Do I need simulink to model the risks of an option portfolio

I wish to buy Matlab Home and learn to model the risks of a derivatives portfolio and then stress test it. So I am guessing I will need : Stochastic calculus Linear algebra Stats/Probability Some ML ...
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1answer
95 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
50 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
130 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
359 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
145 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
91 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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1answer
123 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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1answer
198 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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0answers
7 views

Difference in implied volatility calculation

I've been using vollib to calculate IV, but my answers have been different by tenths from other sources like NASDAQ and Yahoo. The answers range +- 0.5, sometimes even more. The inputs are: $S$ ...
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0answers
83 views

Ideas for speeding up greek calculations

My current calculations using the vollib library averages 0.5 seconds. Is there any way to get it faster? Any tips/best practice notes will be helpful. This is for a scripting language such as ...
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0answers
47 views

Analytical solution to the Black-Scholes equation with time-dependent volatility

I am stuck with the following exercise and I would appreciate any help with it. I have to calculate the analytical function for the price of a call option given the following process for the ...
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1answer
58 views

option time value in the pricing models

option price = intrinsic value + time value where intrinsic value (in other words payoff at N) is defined generally as difference between the underlying asset price and strike price (order depending ...
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1answer
62 views

How to calculate confidence interval for option price?

I model option prices for European call using Monte Carlo method. What is the proper way to calculate the confidence interval? A. -> Calculate the payoffs (there will be number of zeros as some ...
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0answers
20 views

Price of call (calibration)

I need to understand how we got this : $\forall i \in I $ $C^{*}_{0}(T_i,K_i)=e^{-rT_i}E[(S_{T_{i}}-K_i)^+|S_0]=e^{-rT_i+X_{T_{i}}}E[(S_{T_{i}}-K_i)^+]$ at How we pass from conditional expecation to ...
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0answers
24 views

Solving Black Scholes PDE using Laplace transform with barrier up and in, up and out call option

I tried to finish the option pricing in european barrier up and in, up and out call option using Laplace transform. The barrier option there is a boundary condition. Can you explain step by step ...
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1answer
70 views

Calculating the volatility for Black Scholes

The following problem is from the book by Hull. I did it but I am not sure it is right. I am hoping that somebody here can tell me if I did it right and if not where I went wrong. Thanks Bob ...
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0answers
22 views

Two-period pricing of a European put via riskless portfolio

The current price of a stock is $40. It is known that it either increases or decreases by 12.5% every 3-months over the next 6-month period. The risk-free rate of interest is 8% per annum ...
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0answers
81 views

Calculating historical implied volatility

I know that each individual option has it's own implied volatility, but how do you go about calculating the overall implied volatility for an underlying? For example when someone sais the IV of a ...
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0answers
29 views

Price a Fixed Strike Lookback Call Option

I'm having an issue working out the following: Consider a three-period asset price model with interest rate 1+r =6/5 in each period. The initial price of the asset is 4 dollars, while in each period ...
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0answers
37 views

How to find the fx lookback floating/fixed strike options prices?

Currently, I'm working on my thesis in which I'm trying to describe how are the FX lookback options priced. I need to find the real ...
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2answers
101 views

Why the value of this portfolio is negative? [closed]

Let's assume I buy 1 call with strike 100 and 1 call with strike 120 I sell 2 calls with strike 110 (with same expiration) I wonder why value of this portfolio is negative at $t=0$?
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0answers
70 views

Discrete Hedging of Options

Assume that a stock $S_t$ follows simple geometric Brownian motion. Let's say we sold option whose payoff is $f(S_T)$. Now, we are only allowed to trade 2 times in the interval [0,T]. What kind of ...
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65 views

Examples for the option model validation

When implementing a code for the new model, even if it provides sensible price, it is still a good idea to compare it against some benchmarks, even in the special case of constant volatility ...
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1answer
300 views

Which distribution do I get?

Let's assume the stock moves according to a classic Black-Scholes model, and makes a proportional jump with an unknown proportion. Say, it is either +1% or -3% of the stock value, and we know for sure ...
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0answers
45 views

What's the risk-neutral expectation of the arithmetic average of stock price?

All Black-Scholes assumptions apply ($y$ is yield): what's $E(A_T), E(A_T^2)$ and $Var(A_T)$ where $A_T=\frac{\int_0^T S_tdt}{T}$ is the continuous-sampling arithmetic average of the stock price ...
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0answers
21 views

Risk neutral pricing formula justification in incomplete markets [duplicate]

I'm having trouble understanding how to justify the use of the risk-neutral pricing formula $V(t) = \mathbb{E}^{*}[e^{r(T-t)}H(S_{T})|\mathcal{F}_{t}]$ in models which are characterized by ...