FTSE 100 UK (price target)

Price target Bias of 8700-8800 next week.

Key Findings:

1. Volatility & Standard Deviation: Moderate volatility (σ = 120.45), indicating price movements within ±120 points around the mean.
2. Price Clusters: Significant price clustering around the 8,100–8,200 and 8,400–8,500 ranges, suggesting key support and resistance levels.
3. Mean Reversion: A 1.4% daily mean reversion rate, indicating prices tend to revert to the mean (8,547.35) relatively quickly.
4. GBM & Jump Diffusion: Prices expected to stay between 8,400–8,700, but sudden price jumps may occur due to news or macroeconomic events.
5. GARCH Model: Volatility clustering expected, meaning high volatility periods may follow others.
6. Monte Carlo Simulation: A 95% probability range of 8,300–8,800 for the next 7 days.

Day-Trading Strategies:

1. Mean Reversion Strategy: Buy when prices are below the mean (e.g., < 8,450) and sell when above (e.g., > 8,650). Tight stop-loss orders to limit losses.
2. Breakout Strategy: Enter long if prices break above 8,500, or short if below 8,100. Use stop-loss orders near breakout levels.
3. Volatility Trading: Use options (straddles/strangles) around major economic events to profit from unexpected volatility.
4. Momentum Strategy: Trade with the prevailing trend (long in uptrend, short in downtrend). Use stop-loss orders to manage reversals.
5. Range-Bound Strategy: Buy near support (8,100) and sell near resistance (8,500), with tight stop-loss orders if the price breaks out of the range.

Breakout Strategy: (Primary strategy)

• Setup: If the price approaches or breaches resistance around 8,500, you could take a breakout position to capitalize on upward momentum towards your target range.
• Execution: Enter a long position if the price breaks above 8,500 with high volume, signaling the potential for a move towards your target.
• Risk Management: Set a stop-loss just below 8,500 to protect from false breakouts or reversals.

Range-bound Strategy (For implied and historical oscillations):

• Setup: While waiting for the price to reach 8,700–8,800, you can take advantage of price oscillations between support (8,100) and resistance (8,500). Buy near 8,100 and sell near 8,500.
• Execution: Use the price range to enter multiple trades, capturing smaller moves within the established range, while maintaining an eye on the breakout upwards toward 8,700–8,800.
• Risk Management: Set stop-loss orders around the outer bounds of the range to avoid significant losses if the price breaks out.

Volatility Strategy (if expecting news or events):

• Setup: In anticipation of economic or geopolitical events (such as the positive sentiment in economic performance) could trigger volatility, consider using options (straddles or strangles) to profit from potential spikes.
• Execution: Enter straddle or strangle positions ahead of key events, hedging for volatility around your target price range.
• Risk Management: Limit the size of options positions to control risk. Close positions if volatility does not materialize.
• A straddle is an options strategy where you buy a call and a put with the same strike price and expiration date, betting on large price movements in either direction. A strangle is similar but involves buying a call and a put with different strike prices, typically making it cheaper than a straddle. Both strategies are used to profit from volatility, but a strangle requires a larger price move to be profitable, while a straddle benefits from any significant movement in either direction.

Fundamental considerations:

Continued positive economic outlook seems to provide a strong bullish case which further strengthens the bias play towards 8700-8800. THe analysis, baed on the computational details do however suggest turbulent volatility from here to there. No strict timeline is offered for the price target, but the data suggests with a 95% confidence level that prices will reach 8650, this coming week or 2

Below I have attached the snippet of the code I used to compute the the results listed in the findings above, you may review the syntax and confirm whether or not I have accurately made use of the stochastic processes and relevant calculations. I have ommitted the sections of the code that follow my own code signature. For any Quant who wishes to test the instruments and my application of them, please reference the following code box below:

#Mathematical breakdown of the computations

        # 3. Mean Reversion Rate
        mean_reversion_rate = (abs(data['Price'] - mean_price) / mean_price).mean()
        st.write(f"Mean Reversion Rate: {mean_reversion_rate:.4f} (or {mean_reversion_rate * 100:.2f}%)")

        # 4. Geometric Brownian Motion (GBM)
        def gbm_simulation(S0, mu, sigma, days, n_simulations):
            dt = 1 / days
            price_paths = np.zeros((days, n_simulations))
            price_paths[0] = S0
            for t in range(1, days):
                rand = np.random.normal(0, 1, n_simulations)
                price_paths[t] = price_paths[t - 1] * np.exp((mu - 0.5 * sigma**2) * dt + sigma * np.sqrt(dt) * rand)
            return price_paths

        st.write("### Geometric Brownian Motion (GBM) Simulations")
        S0 = data['Price'].iloc[-1]  # Latest price
        mu = data['Price'].pct_change().mean() * 252  # Annualized drift
        sigma = std_dev / mean_price * np.sqrt(252)  # Annualized volatility
        days = 7  # Next 7 days
        n_simulations = 1000  # Number of simulations

        gbm_paths = gbm_simulation(S0, mu, sigma, days, n_simulations)

        fig, ax = plt.subplots()
        ax.plot(gbm_paths)
        ax.set_title("GBM Simulations")
        ax.set_xlabel("Days")
        ax.set_ylabel("Price")
        st.pyplot(fig)

        # 5. Jump Diffusion Model
        def jump_diffusion_simulation(S0, mu, sigma, lambda_jump, mu_jump, sigma_jump, days, n_simulations):
            dt = 1 / days
            price_paths = np.zeros((days, n_simulations))
            price_paths[0] = S0
            for t in range(1, days):
                rand = np.random.normal(0, 1, n_simulations)
                jump = np.random.poisson(lambda_jump * dt, n_simulations) * np.random.normal(mu_jump, sigma_jump, n_simulations)
                price_paths[t] = price_paths[t - 1] * np.exp((mu - 0.5 * sigma**2) * dt + sigma * np.sqrt(dt) * rand + jump)
            return price_paths

        st.write("### Jump Diffusion Simulations")
        lambda_jump = 0.05  # Jump frequency
        mu_jump = 0.01  # Mean jump size
        sigma_jump = 0.02  # Jump volatility

        jump_paths = jump_diffusion_simulation(S0, mu, sigma, lambda_jump, mu_jump, sigma_jump, days, n_simulations)

        fig, ax = plt.subplots()
        ax.plot(jump_paths)
        ax.set_title("Jump Diffusion Simulations")
        ax.set_xlabel("Days")
        ax.set_ylabel("Price")
        st.pyplot(fig)

        # 6. GARCH Model
        st.write("### GARCH Model (Volatility Forecasting)")
        returns = data['Price'].pct_change().dropna()
        garch_model = arch_model(returns, vol='Garch', p=1, q=1)
        garch_fit = garch_model.fit()
        st.write(garch_fit.summary())

        # Forecast volatility
        forecast = garch_fit.forecast(horizon=days)
        forecast_volatility = np.sqrt(forecast.variance.iloc[-1])
        st.write("Forecasted Volatility (Next 7 Days):")
        st.write(forecast_volatility)

        # 7. Monte Carlo Simulation
        st.write("### Monte Carlo Simulations")
        monte_carlo_paths = gbm_simulation(S0, mu, sigma, days, n_simulations)
        monte_carlo_final_prices = monte_carlo_paths[-1]
        confidence_interval = np.percentile(monte_carlo_final_prices, [2.5, 97.5])
        st.write(f"95% Confidence Interval for Final Price: {confidence_interval}")

        fig, ax = plt.subplots()
        ax.plot(monte_carlo_paths)
        ax.set_title("Monte Carlo Simulations")
        ax.set_xlabel("Days")
        ax.set_ylabel("Price")
        st.pyplot(fig)

        # 8. Day-Trading Strategies
        st.write("### Day-Trading Strategies")
        latest_price = data['Price'].iloc[-1]
        support = st.number_input("Enter Support Level", value=8100.0)
        resistance = st.number_input("Enter Resistance Level", value=8500.0)

        # Mean Reversion Strategy
        def mean_reversion_strategy(price, mean_price, threshold=0.01):
            if price < mean_price * (1 - threshold):
                return "Buy"
            elif price > mean_price * (1 + threshold):
                return "Sell"
            else:
                return "Hold"

        # Breakout Strategy
        def breakout_strategy(price, support, resistance):
            if price > resistanc
                return "Buy (Breakout)"
            elif price < support:
                return "Sell (Breakdown)"
            else:
                return "Hold"

        st.write(f"Mean Reversion Strategy: {mean_reversion_strategy(latest_price, mean_price)}")
        st.write(f"Breakout Strategy: {breakout_strategy(latest_price, support, resistance)}")

    else:
        st.error("The uploaded file must contain a 'Price' column.")
else:
    st.write("Please upload a CSV file to get started.")        

Conclusion

If price breaks comfortably above 8500 then we are looking at continued bullish momentum with retracements mirroring the mean reversion rate listed above with a target of 8700 -8800 suggested by the data. Volatility suggests it will not be a smooth ride, so trades in both directions with a bullish bias are the best day trading approach.