# Tagged Questions

Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

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### Show that formula for European call option satisfies Black-Scholes equation and boundary conditions.

Can anyone please help me out with this question? Show that the formula for the European call option satisfies the Black Scholes equation, and that it satisfies the appropriate initial and boundary ...
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### Replication in the multi-period binomial model.

For the solution: Just wanted to ask for $V_{3}(HTH)$ I get $S_{1}(H)$ and $S_{3}(HTH)$ to give me the same maximum value of $16$ so would it also be right if I used $S_{1}(H)$ nstead of $S_{3}(HTH)$?...
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### Compound Interest Formula adding annual contributions

I'd like to know the compound interest formula for the following scenario: P = Initial Amount i = yearly interest rate A = yearly contribution or deposit added. n = the deposits will be made for 10 ...
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### Pricing Function is convex

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 ...
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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 $... 2answers 27 views ### Annuities and interest conversion I am having trouble understanding how to find the equivalent rate of interest per payment periods for annuities. For example, for this question: Find the accumulated value at the end of four years ... 1answer 21 views ### IRR for Incremental Investment Doubt I had a doubt in the following question's solution: Aren't the signs in the equation wrong? Shouldn't it be$-(6,000,000 - 400,000) + 15,000,000(P/F, i^*,15) - 400,000(P/A,i^*,14) = 0(using ... 1answer 44 views ### Derive an expression for the value of the asset as a function of time, V(t), t>=0 An investor deposits USD 300 in a bank account at time 0, reinvests all interest payments and also additionally continuously invests USD 300 per annum, until the total value of the deposits reaches ... 2answers 24 views ### Nominal annual interest A bank offers the following certificates of deposit: \begin{array}{c|lcr} \text{Term in years} & \text{Nominal annual interest rate(convertible semi-annually)} \\ \hline 1 & 0.05 \\ 2 &... 1answer 20 views ### Annuity and future equivalent values I need some clarification on the formulas to use for these questions. Q1. If \30,000 is deposited now into a savings account that earns 7\% per year, what uniform annual amount could be ... 0answers 21 views ### Intuition behind a market uncertainty represented by a filtered complete probability space? What is the intuition behind a market uncertainty represented by a filtered complete probability space (\Omega, F, P, {F_t}), on which an m-dimensional standard Brownian Motion W(t) = (W_1 (t), W_2 ... 1answer 41 views ### Financial Mathematics problem. Consider a property developer who buys a property at time 0 for \90,000. He also spends \10,000 at time 0 to buy some materials he will use to develop the property. Ignoring Inflation , the ... 1answer 21 views ### Ordinary Annuity future value I have a problem to calculate future value of this problem: "The parents of a newborn baby set up an account to cover the cost of college they deposited 1,500 every birthday in an account that pays 8%... 0answers 36 views ### Find the value of forward contract The current spot gold price is \1788 per ounce. The storage cost is \24 per ounce per year, to be paid quarterly at the beginning of each quarter. Suppose the current 3-month and 6 month ... 1answer 19 views ### Need to find annual payment in 2 halfs of the payment period [closed] A loan of 4000 is to be repaid over a period of 8 years. During the first years, exactly half of the loan principal is to be repaid (along with accumulated compound interest) by a uniform series of ... 1answer 47 views ### Finding implied interest rate from swap exchange Suppose the current term structure of interest rates (0.5 year, 1 year, 1.5 year, 2 year maturities annualized with semi annual compounding) is (5.00%, 6.00%, 7.00%, 8.00%). A 2-year vanilla interest ... 1answer 26 views ### loan repayment involving added amounts A bank charges 5\% interest p.a on loan. At the end of the year, the interest is added and then a fixed amount R is paid off. If the amount borrowed is 1000, show that the amount owed at the ... 1answer 40 views ### Financial mathematics - earning compound interest This I assume is a very simple question but can't really wrap my head around it. So the question is: If 100 dollars is deposited at time t = 0 into an account earning 10% interest and 20 is ... 1answer 34 views ### how to prove that there is no arbitrage if the following inequality is satisfied? The continuously compounded interest rate is r. The current price of the underlying asset is S(0), and the forward price with delivery time in one year is F(0,1). Short selling of the stock ... 2answers 65 views ### Simply this formula Is there a way to write \sum_{n=a}^b (Q+P(n-1)) v^n in terms of \sum_{n=a}^b v^n? So far I've gotten: (Q-P)\sum_{n=a}^b v^n + P\sum_{n=a}^b nv^n. *I know the last term can be rewritten as ... 1answer 34 views ### Future value and simple interest On a loan of 3,000 at an interest rate of 12% per year when half of the loan principal is repaid as a lump sum at the end of four years and the other half is repaid in one lump sum amount at the end ... 0answers 38 views ### what am I doing wrong when finding the weights of the market portfolio? I need to find the weights of the market portfolio with three risky securities given the following information: \mu_1=0.08 \sigma_{1}^{2}=0.0255 c_{12}=0.00225 \mu_2=0.1 \sigma_{2}^{2}=0.... 1answer 33 views ### How do I calculate the delivery price for a forward contract? How do I calculate the delivery price for a forward contract? In the time interval [0,t] the interest rate is r_1 and in the time interval [t,T] the interest rate is r_2. Determine the ... 1answer 30 views ### Sum of Present value [closed] The sum of the present value of 1 paid the end of n periods and 1 paid at the end of 2n periods is 1. Find (1+i)^{2n}. Present value for n periods is given as (1+i)^{n} and that of 2n follows the ... 1answer 15 views ### Compounded discount rate The total amount of a loan to which interest has been added is 20000. The term of the loan was for 4.5 years. If the annual rate of interest was 6\% and interest was compounded annually, what ... 2answers 17 views ### Present value and discount function What deposit made today will provide for a payment of \1000 in 1 year and \2000 in 3 years, if the effective rate of interest is 0.075. Answer is \2540.15 I have calculated d=0.069 ... 2answers 57 views ### Compound interest with penalty in withdrawal amount Carl puts 10000 into a bank account that pays an annual effective interest rate of 0.04 for 10 years. If a withdrawal is made during the first five and a half years, a penalty of 5\% of the ... 1answer 23 views ### Expectation equals to Black-Scholes Equation Let S_t be ageometric brownian motion with parameters \sigma and r and fix T,K\in (0,\infty). How can I show that: \begin{align} \mathbb{E}[e^{-rT}max\{(S_T-K),0\}] & = x\Phi(d_+(T-t,x))... 1answer 36 views ### How do you calculate the breakeven amount for two credit cards with different fees and rebates? Credit Card (CC) M offers a rebate of cash back of a dollars, with NO annual fee. CC S offers a rebate of cash back of b dollars, but charges an annual fee of f. How much must I spend ... 1answer 36 views ### Empirical Formula for Financial problem I have a financial problem, which is strictly related to math of course. The problem states that on the last year the steel market price was about 450 \, and a company, that sells steel, used to ... 0answers 24 views ### Under which conditions on \sigma_1, \sigma_2 and \rho_{12} the minimum variance portfolio involves no short selling? If \rho_{12} \lt 1 or \sigma_1 \ne \sigma_2 then \sigma_{V}^2 representing the variance of the portfolio with weights (w_1, w_2)=(s, 1-s) as a function of s attains its minimum value at... 2answers 75 views ### Does the term “selling price” mean the “cost price” or the “sale price” of a product/commodity? I have been told that the idiom "selling price" is the same as the cost price of an item, that is the amount which a seller pays to, e.g. a wholesale merchant. The seller later sells the commodity at ... 5answers 41 views ### How to calculate the price of a product without the sales tax, if we know the price including the tax and the rate of the tax? The question is The price of a mobile phone is8800 inclusive of a 10% GST (General Sales Tax). What is the original price of the mobile phone? This is how I approached it: The Sale Price <...
Consider three securities with the following expected returns, standard deviations of returns, and correlations between returns:  \begin{matrix} \mu_1=0.20, & \sigma_1=0.31, & \rho_{12}=\...