Questions about models for the valuation of option contracts.

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139 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
79 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
762 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
115 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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181 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
397 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
32 views

Delta hedging cost of exotic options?

I'm simulating dynamic delta hedging for up-and-out call option. For plain vanilla call options, I heard that the option price is the expected value of the accumulated delta hedging cost. Does it also ...
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1answer
108 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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33 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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20 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 ...
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0answers
65 views

Black-Scholes formula with deterministic interest rate and dividend yield

Does any one have the Black-Scholes formula for a European call with time-dependent but deterministic interest rate and dividend yield ?
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41 views

Benchmarking option pricing under stochastic interest rates

I priced a long-term option (10 or 20 years) using two different models: one assumes constant interest rates, the other assumes stochastic interest rates. Is there a way (e.g. a benchmark) to ...
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43 views

“Hedging” a put option, question on exercise

I have a question on the following exercise from S. Shreve: Stochastic Calculus for Finance, I: Exercise 4.2. In Example 4.2.1, we computed the time-zero value of the American put with strike ...
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1answer
57 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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0answers
65 views

Vanna-Volga Adjustment

I'm reading Uwe Wystup's "FX Options and Structured Products" to understand Vanna-Volga pricing, which, in his book Chapter $\S3.1$ is called "The Trader's Rule of Thumb". I generally got the idea ...
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0answers
25 views

Multinomial Representation Theorem

In the context of pricing models, the Binomial Representation Theorem (BRT) tells us if we have a binomial price process $S$ that is a $\mathbb{Q}$-martingale (MG), and any other $\mathbb{Q}$-MG $M$, ...
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45 views

Binomial function use in Bezier smoothing

I am using the Bezier method to smooth option volatility curves, which utilised the binomial distribution. Is someone able to clearly explain the interpretation of the binomial distribution in the ...
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1answer
129 views

Binomial tree vs trinomial tree in pricing options

Very new to pricing models. Is there a general guideline when to use binomial tree and when trinomial tree is preferred? As far as I know, unlike binomial tree, trinomial tree only gives a range ...
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2answers
86 views

Annual dividend yield using option prices

If I have only strike, call and put prices for European options, how do I work towards computing the continuous dividend yield?
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35 views

Invoice Discount pricing model

I was wondering whether there exist pricing models in particular for Invoice Discounting contracts and short-term financing solution where credit risk plays a major role. Specifically, assuming that ...
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0answers
24 views

Price a put option on a CPPI

I want to price a put option on a CPPI using Monte Carlo. I have found so far this article which prices a call on a CPPI. I was wondering if I could use the put/call parity here, and and if so, how ...
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0answers
6 views

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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1answer
100 views

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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34 views

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 ...
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12 views

Will implied volatilities rise by same amount across time and across strikes in lieu of an earnings report or a news event

It is said that implied volatility of an option rises leading up to an earnings report or a pending news event like FDA trial, a possible takeover,elections(?) etc. My question is, implied volatility ...
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41 views

Complicated American style option contract with numerous non-standard features (simultanous exercise, additional premium, etc.)

I want to value the following contract for times $0<t<T$, i.e. determine $V(t,\cdot)$ where $\cdot$ refers to all other dependences (strike, spot, volatility, etc.). The contract is long and ...
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56 views

How to value an expansion option?

Fair warning this is help with homework. I am not asking for an answer but some guidance or a formula would be nice. I have absolutely no background in finance and this class is online with no ...
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30 views

How to calculate intraday implied vol on the last day of trading an OTM option

i've been trading globex options on US Treasury futures, but my option calculator only takes the date as the time input..so on the last trading day, the model assumes all values are errors because the ...
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58 views

Pricing defaultable binary option with hazard rate approach

I'm studying defaultable claims and asked myself how to price a digital payoff. Consider an option paying $1$ at maturity in case of non-default before maturity and if a given underlying process $S$ ...
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27 views

Real-World Cash Account Implementation and Return

Often in financial math, the concept of the risk-free cash account, with return R, is invoked as an instrument for calculating prices - when constructing an option-replicating portfolio, for example. ...
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1answer
85 views

Pricing options with two assets

I'm studying for a test and am stuck on this practice question: With interest rates equal to 0, two different stocks $S_1$ and $S_2$, both valued at \$1 today, can be worth \$2 or \$0.50 at some ...
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0answers
368 views

R or Matlab code for Multi-Barrier-Options (3 or more underlyings)

I am looking for R or Matlab code examples of multi-barrier-options (or multi-barrier reverse convertibles) with at least 3 underlyings. Do you have such code or can you point me to a place where I ...
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112 views

The basic principle of the construction a portfolio of options

I have a question like this. Assume today's date is 9 January 2016 and XYZ's share price stands at $10. On 8 November 2016 there is a Presidential election and you believe that depending on who is ...
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1answer
221 views

How to construct the binomial model for European option?

The annual interest rate is 5.3% and the annualized volatility of a non-dividend paying stock over the next six months will be 12.5% (annualized). i) Construct binomial trees of 5, 10 and 30 periods ...
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2answers
270 views

Change option B&S pricing

Consider a market composed by two stocks whose prices $X$ and $Y$ are given by B&S diffusion $$dX_t= \mu X_t dt+ \sigma X_tdW_t$$ $$dY_t= \mu Y_t dt+ \sigma Y_tdB_t$$ Supposing the market is ...
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1answer
51 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
59 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 ...
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1answer
71 views

Show that the equation solves the Black-Scholes PDE

I have the solution as given Based on this, I have to show that this solves the Black-Scholes formula It means that I should take the partial derivatives of the solution above and then receive the ...
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4answers
2k views

True or False? An option's price will always be greater than or equal to its intrinsic value

Since if the option's price is lower than its intrinsic value (eg. strike price - current stock price for puts), then an arbitrage opportunity arises from buying the option at bargain and then ...