MindMap Gallery Financial Mathematics Formulas
This is a mind map about Financial Mathematics Formulas, Main content: Financial Risk Management, Derivatives Pricing, Equity Valuation, Bond Pricing and Yield, Asset Pricing Models, Risk and Return, Investment Return and Yield, Interest and Discounting, Time Value of Money.
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This infographic, created using EdrawMax, outlines the pivotal moments in African American history from 1619 to the present. It highlights significant events such as emancipation, key civil rights legislation, and notable achievements that have shaped the social and political landscape. The timeline serves as a visual representation of the struggle for equality and justice, emphasizing the resilience and contributions of African Americans throughout history.
This infographic, designed with EdrawMax, presents a detailed timeline of the evolution of voting rights and citizenship in the U.S. from 1870 to the present. It highlights key legislative milestones, court decisions, and societal changes that have expanded or challenged voting access. The timeline underscores the ongoing struggle for equality and the continuous efforts to secure voting rights for all citizens, reflecting the dynamic nature of democracy in America.
This infographic, created using EdrawMax, highlights the rich cultural heritage and outstanding contributions of African Americans. It covers key areas such as STEM innovations, literature and thought, global influence of music and arts, and historical preservation. The document showcases influential figures and institutions that have played pivotal roles in shaping science, medicine, literature, and public memory, underscoring the integral role of African American contributions to society.
Financial Mathematics Formulas
Time Value of Money
Present Value (PV) and Future Value (FV
Future Value Formula: FV = PV (1+r)^n
Example: FV = 1157.63 for a deposit of 1000 CNY at 5% annual interest for 3 years
Present Value Formula: PV = FV / (1+r)^n
Example: PV = 125,000 for an annual payment of 10,000 CNY with a discount rate of 8%
Annuities
Future Value of Ordinary Annuity: FV = A ((1+r)^n -1)/r
Present Value of Ordinary Annuity: PV = A (1-(1+r)^-n)/r
Perpetuity: PV = A / r
Example: PV = 125,000 for an annual payment of 10,000 CNY with a discount rate of 8%
Interest and Discounting
Simple Interest: P * r * t
Compound Interest: A = P * (1 + r/m)^(m*t)
m = number of compounding periods per year
Continuous Compounding: A = P * e^(r*t)
Example: A ≈ 11,274.1 for a principal of 10,000 CNY at 6% annual interest over 2 years with continuous compounding
Investment Return and Yield
Single Period Return: R = (P1 - P0 + D) / P0
Geometric Average Return:(1+R_avg) = nth_root(Π(1+R_i))
Internal Rate of Return (IRR): NPV = Σ(C_t / (1+IRR)^t) - C0 = 0
Example IRR ≈ 9.7% for an investment of 1000 CNY with cash flows of 400 CNY over 3 years
Risk and Return
Expected Return: E(R) = Σ p_i * R_i
Variance: σ^2 = Σ p_i * (R_i - E(R))^2
Standard Deviation: σ = √σ^2
Covariance: Cov(Rx,Ry) = E[(Rx-E(Rx))(Ry-E(Ry))]
Correlation Coefficient: ρ_xy = Cov(Rx,Ry)/(σ_x * σ_y)
Example: Diversifiable risk for Stocks A and B with correlation coefficient = -0.3
Asset Pricing Models
CAPM (Capital Asset Pricing Model)
E(R_i) = R_f + β_i * (E(R_m) - R_f)
β_i = Cov(R_i,R_m) / σ_m^2
Example: Expected return = 9% for a risk-free rate of 3%, market return of 8%, and β = 1.2
APT (Arbitrage Pricing Theory)
E(R_i) = R_f + β_i1*F1 + β_i2*F2 + ... + β_in*Fn
Bond Pricing and Yield
Bond Price: P = Σ(C / (1+y)^t) + F / (1+y)^n
C = coupon payment, F = face value, y = yield to maturity
Yield to Maturity YTM: Solve for yield that equates price to present value
Duration: D = Σ t * PV(C_t) / P
Equity Valuation
Dividend Discount Model (DDM): P0 = D1 / (r - g)
Example: P0 = 33.33 for a dividend of 2 CNY/share, growth rate of 4%, and discount rate of 10%
Price-to-Earnings Ratio (PE Ratio): P = EPS * PE
Derivatives Pricing
Option Pricing (Black-Scholes) Model
C = S0 * N(d1) - X * e^(-rt) * N(d2)
d1 = (ln(S0/X) + (r + σ^2 /2)t) / (σ√t)
d2 = d1 - σ√t
Example: Calculate option value for a stock price of 50, strike price of 52, time of 1 year, σ = 20%, r = 5%
Forward Contract Pricing: F0 = S0 * e^(rt)
Financial Risk Management
Value at Risk (VaR): VaR_α = Z_α * σ_P * V
Expected Shortfall (ES)
Average loss conditional on exceeding VaR