Questions about models for the valuation of option contracts.

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6
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4answers
488 views

Replicating portfolio and risk-neutral pricing for interest rate options

For equity options, the pricing of options depends on the existence of a replicating portfolio, so you can price the option as the constituents of that replicating portfolio. However, I am not seeing ...
0
votes
0answers
5 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 ...
0
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0answers
22 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 ...
0
votes
0answers
18 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 ...
0
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0answers
12 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 ...
3
votes
2answers
180 views

Does higher vega imply higher IV and vice versa

If an option A has higher vega than option B, does that also mean that A has a higher IV than B? I understand that by definition, a higher vega means that A's price is more sensitive to its IV than B. ...
2
votes
1answer
41 views

If an option went down in value, how much is due to theta decay and how much due to fall in IV

Let us say that there was a stock trading at 100 and the 105 call was trading at 3 $. with 1 month to go Now stock went up to 104 after 15 days, and the call dropped to 2.80 $, to the call buyer's ...
0
votes
1answer
25 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 ...
1
vote
1answer
34 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 ...
1
vote
1answer
38 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 ...
0
votes
0answers
10 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 ...
2
votes
2answers
78 views

Time-independent local volatility

Suppose somebody provides us with a surface of European call prices $C(\tau,K)$ where $\tau$ stands for time-to-maturity and $K$ for the strike. By Dupire's results, there is a unique local volatility ...
3
votes
2answers
59 views

Black Scholes: How does it help to transform uncertainty and still not be able to calculate a fair price?

Recapitulating the history of Black-Scholes: Nobody knows the fair price of options. Revolution: BS! You put in all the parameters and get a price -> A Nobel Prize for that one! Wait: Nobody knows ...
1
vote
1answer
36 views

Numerical delta of Bond Options

I'm trying to calculate the delta for bond Call options. I'm using the vasicek model which gives the following solution for a Zero-coupon bond call option: $Z = N P(t,S) \Phi(d_1) - K P(t,T) ...
1
vote
0answers
27 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 ...
7
votes
6answers
3k views

Why Drifts are not in the Black Scholes Formula

This question has puzzled me for a while. We all know geometric brownian motions have drifts $\mu$: $dS / S = \mu dt + \sigma dW$ and different stocks have different drifts of $\mu$. Why would ...
10
votes
4answers
6k views

How should I calculate the implied volatility of an American option in a real-time production environment?

There are many models available for calculating the implied volatility of an American option. The most popular method, employed by OptionMetrics and others, is probably the Cox-Ross-Rubinstein model. ...
1
vote
2answers
94 views

How to price an European call on zero-coupon from the yield curve?

It is known that the price of an European call of maturity $T^*$ on zero-coupon of maturity $T$ is given by $$p(0,T)= B(0,T^*)\mathbb E ^{\mathbb Q_{T^*}}\left[ (B(T^*,T)-K)^+\right]$$ where ...
7
votes
1answer
342 views

How to price a Swing Option?

I'm working in the commodity market and I've to price Swing Options with MATLAB, preferably with finite element. Has anyone already priced these kind of derivatives? I'm thinking about using the ...
0
votes
0answers
12 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 ...
1
vote
0answers
32 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 ...
1
vote
0answers
21 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 $ ...
2
votes
1answer
119 views

option pricing with limitation on the change of underlying daily changes

how are we supposed to price an European option given the fact that the daily return of the underlying is limited within -X% to X%? For example, if X = 5, the price of the underlying cannot go up 8% ...
1
vote
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)^+ ...
2
votes
2answers
148 views

Why do we need $dS_t=r S_tdt+\sigma S_tdW_t^Q$?

Suppose $S_t$ is the stock price and follows the dynamics $$dS_t=\mu S_tdt+\sigma S_tdW_t$$. According to Girsanov, we can apply change of measure and obtain $dS_t=r S_tdt+\sigma S_tdW_t^Q$, this ...
2
votes
2answers
280 views

Pricing an american style option on a bond future

what is the good way to pricing american option on bond future? From bonk fixed income securities 3rd by Tuckman, I understand how to pricing European option on bond future, but I still have no clue ...
7
votes
2answers
3k views

What causes the call and put volatility surface to differ?

I currently have a local volatility model that uses the standard Black Scholes assumptions. When calculating the volatility surface, what causes the difference between the call volatility surface, ...
-2
votes
1answer
38 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 ...
-2
votes
2answers
37 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 ...
0
votes
0answers
36 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 ...
2
votes
2answers
143 views

Is it fair to assume $(ud=1)$ in the binomial tree option pricing model?

I have discussion with my colleague on why a general assumption $$ud=1$$ in binomial tree option pricing model would be necessary? I take it a simplification of the problem, otherwise, there will be ...
3
votes
1answer
124 views

Data Selection for Empirical Pricing Kernel Estimation (Stochastic Discount Factor)

I want to estimate an empirical pricing kernel for an index. Hence, I need to estimate a physical and risk neutral density. For estimating the physical density, only the index data in an observed time ...
2
votes
1answer
128 views

Some questions about implied volatilities and how to generate theoretical prices when market prices are not available

I am building a little Excel file that take some option prices in input and plots the volatility smile/surface. I have a script that reads market prices from the option chain for 3 different ...
2
votes
1answer
82 views

Price an option whose strike price is always lower than the future price of the security

Suppose it is known that the price of a certain security after one period will be one of the $m$ values $s_1,\ldots,s_m$. What should be the cost of an option to purchase the security at time $1$ for ...
1
vote
0answers
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 ...
2
votes
3answers
109 views

Replication of a call option by cash-or-nothing digital option

I am so stuck on this question: Consider a two-asset model where asset 0 is cash, so that the price of asset 0 is $B_t=1$ for all $t \geq0$. Asset 1 has prices given by $dS_t = a(S_t) dW_t$, where the ...
1
vote
0answers
75 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 ...
2
votes
1answer
87 views

Asymptotic behavior of theta of vanilla call option

It is well known that the theta of call option is always negative. Also, the theta of (at the money call option) goes to infinity as the time approaches to the maturity. On the other hands, (ITM and ...
4
votes
1answer
95 views

How to price a futures spread option?

Let's say I have two futures contract $F_1(0,T)$ and $F_2(0,T)$ on two different correlated underlyings. If I assume that both underlying follow a GBM with volatility $\sigma_1$ and $\sigma_2$ ...
4
votes
5answers
2k views

Call vs. Put Option

I have two interrelated questions that have been bothering me for some time. I have read all the stuff online and it still doesn't make sense to me: Let us assume: 0% interest rate (both hedge ...
2
votes
3answers
135 views

Pricing exotic option whose payout depends on the stopping time

I am struggling with this question: Let $B$ be a standard Brownian motion. In a Black-Scholes model, at time $t$, the stock price is given by \begin{equation} S_t = \exp \{ \sigma B_t + ( r- ...
1
vote
3answers
192 views

forward implied volatility skew

I would like to calculate implied forward volatility skew. I have stochastic volatility monte carlo. What kind of payoff do I need to price and how to use Black() formula to calculate the implied ...
1
vote
2answers
101 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 ...
4
votes
1answer
179 views

Analysis of Unbalanced Covered Calls

Hello I am doing an analysis on covered calls with and extra amount of naked calls. Ignore the symbol and current macroeconomic events. I couldn't find any reference to this strategy (unbalanced is ...
1
vote
2answers
104 views

Dupire model and Local Volatility model

In the context of Option pricing model. Is there a difference between the Dupire Model and the Local volatility model ? Thanks Achal
0
votes
1answer
56 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 ...
0
votes
2answers
98 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 ...
4
votes
1answer
335 views

What are the main flaws behind Ross Recovery Theorem?

Stephen Ross’ new paper claims that it is possible to separate risk aversions and historical probabilities if the Stochastic Discount Factor is transition independent using Perron-Frobenius Theorem. ...
7
votes
4answers
788 views

Software for decomposing structured products into plain vanilla products

Nowadays structured products (or packages) with complex payoff diagrams are omnipresent. Do you know of any software, add-ons, apps, code whatever, that enables you to enter a payoff diagram or a ...
1
vote
1answer
52 views

Pricing rule shall be a martingale measure

In the book "Financial Modelling with jump processes" by Cont and Tankov there is a chapter that explains martingale pricing principles. It is not extremely formal, but gives the idea underlying the ...