Questions about models for the valuation of option contracts.

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2
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3answers
81 views

Distribution of pay-off of an exotic option

Can any assumptions be made about the pay-off of an exotic option? For example, might we say the distribution of the pay-off a vanilla option would be Normal? I have built a valuation tool that ...
2
votes
0answers
45 views

Capital increase: which stock price to use as input to Black-Scholes formula?

For an exercise we have to calculate the theoretical value of a scrip / preferential right on its issue day (23 April) in the context of a capital increase. The scrips are issued on 23 April. The ...
9
votes
1answer
166 views

How do different models impact option Greeks?

If I trade an option using delta, vega, Prob OTM, etc. these are derived from a model. How do leading models impact valuations in terms of the Greeks? I suppose to form a baseline it would have to be ...
1
vote
2answers
79 views

Counting random paths

Assume the path of a certain stock can be modeled using a binomial tree. The initial price of the stock at time $t=0$ is 1024. The upstage factor of the stock price is $x=1.25$ and downstage factor of ...
2
votes
1answer
56 views

Option pricing: Risk neutral probability calculation

Let $u=1.3$ $d=0.9$ $r=.05$ $S(0)=50, X = \text{strike} = 60$. Assume binomial model Why isn't the risk neutral probability found by solving the following for $p$: $$E[S(T)]=p65+(1-p)45=S(0)(1+r)^T=...
1
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1answer
92 views

Monte Carlo Option Pricing: Averaging Price Per Path

In Glasserman's book, he computes the price of an option by first computing the average price over each simulated price path. Once all the paths have been simulated, the average of all the payoffs is ...
0
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0answers
13 views

Proving the convexity of put price [duplicate]

Prove that the price of the European put option is a convex function of the strike price in one-step binomial model. In other words, if $P_E(X)$ is the price of the European put option in one-step ...
0
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0answers
44 views

Portfolio replication option pricing: Money market position

Why when replicating a call option, the money market position (bond, risk free investment) is negative and when replicating a call option, the money market position is positive? Please explain ...
1
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1answer
57 views

Put-on-call option confusion

So the question asks: Given a 3-steps Binomial Tree model with $S(0) = 50$, $U = 20%,D = ō€€€20%$, and $R = 5%$. A European call option has the strike price $X = 40$ and maturity time $T = 3$. Also, a ...
1
vote
1answer
44 views

Put call parity: when are the premiums the same?

Please explain why put call parity could be compared to the payoff of a long forward contract. ie. $C_E-P_E=V_X(0)$ where $C_E,P_E$ are the call/put premiums and $V_X(0)$ is the value of a long ...
0
votes
1answer
73 views

Replication strategy of European call option

So the question asks: L et $S(0) = 120$ dollars, $u = 0.2$, $d = āˆ’0.1$ and $r = 0.1$. Consider a call option with strike price $X = 120$ dollars and exercise time $T = 2$. Find the option price and ...
0
votes
0answers
34 views

Connecting Call price computed discretely to call price computed under continuous time case

I want to connect the call premiums calculated discretely via the binomial pricing method to the Black-Scholes-Merton formula for the call premium which applies to continuous time case. The framework ...
3
votes
3answers
97 views

Construct option and stock portfolio

If a riskless security costs 100 today and will cost 120 at time T, a stock costs 50 today and will either be 70 or 30 at time T, and call options on the stock have strike price 50 expiring at time T, ...
6
votes
2answers
214 views

The Upper Bound of an American Put Option

I have just read the following paragraph (in bold) and have a question on the upper bound of an american put option: http://www.sharemarketschool.com/option-valuation-upper-and-lower-bounds-part-...
3
votes
5answers
377 views

Estimate probability of limit order execution over a large time frame

I have a negligible amount of money (\$5000) that I would like to invest in a stock. I would like to buy the stock at some point in the next year, and get the lowest possible price. I would like to ...
1
vote
2answers
147 views

Why is the term structure of the implied volatility surface non-monotonic?

Does this reflect expectations & uncertainty about interest rates (exposure to rho?), event driven concerns about the underlying, or something else?
1
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0answers
53 views

Binary American Call Option (Cash or Nothing)

Suppose we have a stock with current price $S(0)=X$ and the interest rate is zero. When the stock reaches level $\$ H$ for the first time ($H>X$), the option can be exercised and its payoff is $\$ ...
0
votes
3answers
78 views

Linear combination of payoffs of bull and bear spreads

Write the following payoffs as linear combination of call options with different strikes and possibly some cash and give the closed form formula for them. Attempted solution: The payoff for the bear ...
3
votes
1answer
112 views

Why are there two expressions for the Black-Scholes hedging portfolio

I am new to derivatives pricing and am trying to understand why there are two different expressions for the Black-Scholes hedging portfolio. The first approach, used in books like Hull, stipulates ...
1
vote
1answer
57 views

A clarification on the Heston option pricing formula

I have carefully reconstructed all the computations that lead to the Heston option pricing formula for a call. I end up with this formula for the "adjusted" probabilities $$ P_j\left(x,v,T;\ln K\...
0
votes
1answer
36 views

Known future volatility and difficulty in predicting final P/L

I have started Chapter 1 of Dynamic Hedging by Taleb and it starts by saying "Even if traders knew the exact future volatility but hedged themselves (rebalanced the gamma) at discretely spaced ...
1
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0answers
40 views

Pricing function $P(S,t)$ is convex in $S$ for all $t$

I am now reading Alternative Characterization of American Put Options by Carr et all (available at http://www.math.nyu.edu/research/carrp/papers/pdf/amerput7.pdf). There is a theorem called 'Main ...
4
votes
1answer
84 views

Lookback option to find stock price

Consider the payoff equation for the lookback option $\psi(T)= max(S_t-S_T)$, where $t\in[0,T]$ and $S_t$ is modeled by the geometric Brownian motion with constant parameters. Find the price of stock ...
1
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1answer
52 views

Potential Arbitrage profit or proof problem

So the question asks: Consider 4 following European call and put options with the same maturity time: Call option with strike price $100$ sell for $45$ Call option with strike price $110$ sell for $...
0
votes
1answer
56 views

Interpolating on the BS parameters and injecting in the BS formula vs interpolating directly on option prices

Let's consider a simple European call option. In practice, the way the Black-Scholes formula is used to price it is by injecting all of the parameters and paying special attention to the volatility ...
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0answers
50 views

Euler discretization bias, heston model

I am performing option pricing using Heston model and Euler discretization. I'm getting the following result: ...
6
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0answers
76 views

recent developments in American options?

I have read the paper written by Egloff (2005) using machine learning techniques to solve the optimal stopping problem. Is there any development in pricing American options during 2005-2016? (based ...
5
votes
3answers
135 views

Binary Option in B-S model - technical question

I want to price Binary Option in Black-Scholes model. The payoff is of the form $f(S_{T})=I_{\{S_{T}-K>0\}}$. If we assume that $t=0$ this is easy, because then we have $C_{0}=\mathbb{E}^{*}\...
2
votes
1answer
98 views

Why is $N(d_2)$ not needed for hedging?

I'm trying to understand delta hedging. If I sell a plain vanilla call option, in order to delta hedge it, I have to buy delta amount of stocks. What I don't understand is that the BS price of the ...
4
votes
1answer
145 views

How to use the Black-Scholes formula with LIBOR rates?

I want to price an FX option using the Black-Scholes model, but I don't know the risk free rate, nor the volatility. I only know the LIBOR rates, the strike, and that the expiration day is 87 days ...
1
vote
2answers
63 views

How to price jumps in payoffs

I specifically want to know how to model a jump condition while valuing a derivative.Example :- the jumps which are observed in digital product payoffs, or barriers and knockouts. Although a ...
4
votes
2answers
99 views

Is complete market or not if appreciation rate is random?

Consider the stock price process satisfies the following SDE: $dS_t=\mu_t S_tdt + \sigma S_t dW_t , S_0=s $ and the appreciation rate process $\mu_t$ satisfies the following SDE: $d\mu_t=(a-\mu_t)...
0
votes
1answer
63 views

Payoff of a butterfly c++

I would like to price options (call, put,, butterfly) with monte-carlo method, but actually I need the expression of the butterflay payoff; Could you ^please help me !
0
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0answers
51 views

Delta hedge compound option

Delta hedge portfolio should be adjusted from one period to the other, as the ratio changes. How does it work with compound options though? Suppose, I have a put on a call option on a stock, in 2 time ...
3
votes
2answers
92 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: $S$ (...
3
votes
1answer
88 views

Approximation of an option price

The value of an option in the money is 11.50 Euros. The parameters of the market are: -The price of the underlying stock: 81.4 Euros. -The volatility ofthe underlying is : 34.65 % The ...
0
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2answers
93 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 ...
0
votes
2answers
155 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 ...
3
votes
1answer
131 views

Example of options that cannot be priced with least-square Monte Carlo

Can you give some example of options that cannot be priced with least-square Monte Carlo? Intuitively, this is any option for which a payoff depends on a previous exercise decision. It's relatively ...
0
votes
1answer
91 views

Black_scholes formula for a butterfly option

Im wondering if I can apply Black-Scholes formula to valorate a butterfly option, i.e: $$B(T)=Vcall(S(T)-K,0)+Vcall(S(T)-K',0)-2Vcall(S(T)-K'',0)$$ with $K<K''<K'$, just evaluating each call ...
1
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0answers
70 views

School project about Black Scholes with stochastic volatility

In a university project I am looking at Black Scholes model with a stochastic volatility. Iā€™m still not quite sure about my focus (I am in the beginning 'Idea phase'). I want to explain the theory ...
0
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0answers
112 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 python....
3
votes
1answer
134 views

Question in “Computational Methods in Finance” by Ali Hirsa - Chapter 2: Derivatives Pricing via Transform Techniques"

Reference: "Computational Methods in Finance" by Ali Hirsa - Chapter 2: Derivatives Pricing via Transform Techniques" - Page 37* Background: The author prices call option using the Fourier Transform. ...
0
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0answers
93 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 ...
0
votes
1answer
51 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 ...
1
vote
1answer
27 views

binomial - parameters at which american option hits early exercise possibility

I am looking for a set of parameters (d,u,r,So,K, N=?) for pricing an american call using binomial where the call hits the early exercise possibility. Do you have any exemplary set?
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1answer
85 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 ...
0
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1answer
61 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 ...
1
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1answer
55 views

Martingale correction for Andersen scheme with Interest Rate

I have implemented martingale correction to my Andersen scheme for Heston model, as it is in the paper (page 19-22): http://www.ressources-actuarielles.net/EXT/ISFA/1226.nsf/0/...
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0answers
96 views

Heston model - Andersen scheme implementation

I would like to implement Andersen scheme for Heston simulation. On the following snipped is my code for generating asset path: ...